Index: palm/trunk/SCRIPTS/compile_tutorial
===================================================================
--- palm/trunk/SCRIPTS/compile_tutorial	(revision 915)
+++ palm/trunk/SCRIPTS/compile_tutorial	(revision 915)
@@ -0,0 +1,155 @@
+#!/bin/ksh
+#------------------------------------------------------------------------------!
+# Current revisions:
+# -----------------
+# Initial revision
+# 
+# Former revisions:
+# -----------------
+# $Id$
+#
+# Description:
+# ------------
+# This script compiles all LaTeX files that are located in TUTORIAL/SOURCE/.
+# Three PDFs are generated for each source file: 
+# the lecture version has a step-by-step layout, the handout version contains 
+# lines for notes, the web version can contain additional comments by the 
+# authors and has no step-by-step layout.
+# If a file is given as input parameter, only this file will be compiled.
+#
+# Execution:
+# ----------
+# compile_tutorial                 --> compiles all *.tex files in directory.
+# compile_tutorial -f filename.tex --> compiles filename.tex only.
+#------------------------------------------------------------------------------!
+
+    cycles=3
+    debug=false
+    file=""
+
+    full_name=`readlink -f $0`
+    directory="$(dirname $full_name)/../TUTORIAL/SOURCE"
+    output_dir="$(dirname $full_name)/../TUTORIAL"
+    cd $directory
+
+    while  getopts  :df: option
+    do
+       case  $option  in
+          (d)   debug=true;;
+          (f)   file=$OPTARG;;
+          (\?)  printf "\n  +++ unknown option $OPTARG \n"
+                printf "\n  --> type \"$0 ?\" for available options \n"
+                locat=parameter;exit;;
+       esac
+    done
+
+    shift OPTIND-1
+
+
+#   Print help
+    if [[ "$1" = "?" ]]
+    then
+       (printf "\n  *** compile_tutorial can be called as follows:\n"
+        printf "\n     compile  -d  -f..\n"
+        printf "\n     Description of available options:\n"
+        printf "\n      Option      Description                                 Default-Value"
+        printf "\n        -d        show all debug output                               false"
+        printf "\n        -f        Filename (single file compilation mode)                \"\""
+        printf "\n         ?        this outline \n\n") | more
+        exit
+    fi
+
+    if [[ "$file" != "" ]] then
+       file_list=`readlink -f $(basename $file)`
+    else
+       file_list="$directory/*.tex"
+    fi
+
+
+    if [[ ! -d $output_dir/LECTURE ]] then
+       printf " $output_dir/LECTURE will be created.\n"
+       mkdir -p $output_dir/LECTURE
+    fi
+
+    if [[ ! -d $output_dir/HANDOUT ]] then
+       printf " $output_dir/HANDOUT will be created.\n"
+       mkdir -p $output_dir/HANDOUT
+    fi
+
+    if [[ ! -d $output_dir/WEB ]] then
+       printf " $output_dir/WEB will be created.\n"
+       mkdir -p $output_dir/WEB
+    fi
+
+    for i in $file_list;
+    do 
+       if [[ "$(echo $(basename $i)|cut -c1-6)" != "header" ]] then
+          printf "\n Compiling $i.\ Please wait..."
+
+#         Check if file exists
+          if [[ ! -f "$i" ]] then
+             printf " error."
+             printf "\n File $i does not exist. Skipping..."
+             break
+          fi
+
+          compiling_type="LECTURE"
+          for (( j=0; j<=2; j+=1 ))
+          do
+             rm -rf tmp_dir
+             mkdir tmp_dir
+             cp header_${compiling_type}.tex header_tmp.tex
+             for (( k=1; k<=$cycles; k+=1 ))
+             do
+                if ( $debug ) then
+                   printf "\n pdflatex output:\n\n\n"
+                   pdflatex -halt-on-error -output-directory=tmp_dir $i
+                   if [[ "$?" != "0" ]] 
+                   then
+                      printf "\n\n Compilation aborted. Please check your source code.\n"
+                      rm -rf tmp_dir
+                      exit
+                    fi
+                else
+                   pdflatex -halt-on-error -output-directory=tmp_dir $i  2>&1 > error_file
+
+                   if [[ "$?" != "0" ]] 
+                   then
+                      printf " error."
+                      printf "\n The following error occured during the compilation:\n\n\n"
+                      cat error_file |grep "Error"
+                      printf "\n\n Compilation aborted. Please check your source code.\n"
+                      rm -rf tmp_dir
+                      rm error_file
+                      exit
+                   fi
+                fi
+                mv tmp_dir/*.pdf $output_dir/$compiling_type
+             done
+             if [[ "$compiling_type" = "LECTURE" ]]
+             then
+                compiling_type="WEB"
+             elif [[ "$compiling_type" = "WEB" ]]
+             then
+                compiling_type="HANDOUT"
+             fi
+          done  
+          printf " done."
+       fi
+
+#      Cleaning up
+       if [[ -f header_tmp.tex ]] then
+          rm header_tmp.tex
+       fi
+       if [[ -f error_file ]] then
+          rm error_file
+       fi
+       if [[ -d tmp_dir ]] then
+          rm -rf tmp_dir
+       fi
+
+    done
+
+    printf "\n\n +++ All actions finished.\n"
+
+exit
Index: palm/trunk/SCRIPTS/release_tutorial
===================================================================
--- palm/trunk/SCRIPTS/release_tutorial	(revision 915)
+++ palm/trunk/SCRIPTS/release_tutorial	(revision 915)
@@ -0,0 +1,72 @@
+#!/bin/ksh
+#------------------------------------------------------------------------------!
+# Current revisions:
+# -----------------
+# Initial revision
+# 
+# Former revisions:
+# -----------------
+# $Id$
+#
+# Description:
+# ------------
+# Script for copying the compiled PDFs to a desired web directory. This script
+# should be used by user raasch only.
+#
+# Execution:
+# ----------
+# release_tutorial --> Copy all PDF files to $release_directory (see below)
+#------------------------------------------------------------------------------!
+
+    release_directory="/home/raasc/public_html/files"
+    mod_dir_lecture="755"
+    mod_dir_handout="755"
+    mod_dir_web="755"
+    mod_lecture="644"
+    mod_handout="644"
+    mod_web="644"
+
+    full_name=`readlink -f $0`
+    directory="$(dirname $full_name)/../TUTORIAL/SOURCE"
+    input_dir="$(dirname $full_name)/../TUTORIAL"
+    cd $input_dir
+
+    printf "\n Files will be released in $release_directory/."
+    printf "\n Subdirectories LECTURE, HANDOUT and WEB will be creared if necessary."
+    printf "\n Start copying...\n"
+
+
+    if [[ ! -d $release_directory/LECTURE ]] then
+       printf " $release_directory/LECTURE will be created.\n"
+       mkdir -p $release_directory/LECTURE
+       chmod $mod_dir_lecture $release_directory/LECTURE
+    fi
+    cp LECTURE/*.pdf "$release_directory/LECTURE/"
+    chmod $mod_lecture $release_directory/LECTURE/*
+    printf " Finished LECTURE.\n"
+
+    if [[ ! -d $release_directory/HANDOUT ]] then
+       printf " $release_directory/HANDOUT will be created.\n"
+       mkdir -p $release_directory/HANDOUT
+       chmod $mod_dir_handout $release_directory/HANDOUT
+
+    fi
+    cp HANDOUT/*.pdf "$release_directory/HANDOUT/"
+    chmod $mod_handout $release_directory/HANDOUT/*
+    printf " Finished HANDOUT.\n"
+
+    if [[ ! -d $release_directory/WEB ]] then
+       printf " $release_directory/WEB will be created.\n"
+       mkdir -p $release_directory/WEB
+       chmod $mod_dir_web $release_directory/WEB
+    fi
+    cp WEB/*.pdf "$release_directory/WEB/"
+    chmod $mod_web $release_directory/WEB/*
+    printf " Finished WEB.\n"
+
+    printf " \n +++ All actions finished.\n"
+
+exit
+
+
+
Index: palm/trunk/TUTORIAL/SOURCE/basic_equations.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/basic_equations.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/basic_equations.tex	(revision 915)
@@ -0,0 +1,407 @@
+% $Id$
+\input{header_tmp.tex}
+%\input{../header_lectures.tex}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{pgf}
+\usetheme{Dresden}
+\usepackage{subfigure}
+\usepackage{units}
+\usepackage{multimedia}
+\usepackage{hyperref}
+\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
+\usepackage{xmpmulti}
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows,positioning}
+\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{multicol}
+
+
+\institute{Institut fÃŒr Meteorologie und Klimatologie, Leibniz UniversitÃ€t Hannover}
+\date{last update: \today}
+\event{PALM Seminar}
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamertemplate{footline}
+  {
+    \begin{beamercolorbox}[rightskip=-0.1cm]&
+     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,
+      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}
+      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}
+    \end{beamercolorbox}
+  }
+%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}}
+
+\title[Basic Equations]{Basic Equations}
+\author{Siegfried Raasch}
+
+\begin{document}
+
+%Folie 1
+\begin{frame}
+   \titlepage
+\end{frame}
+
+
+\section{Basic equations}
+\subsection{Basic equations, Unfiltered}
+
+% Folie 2
+\begin{frame}
+   \frametitle{Basic equations, Unfiltered}
+   \begin{itemize}
+       \item<2->Navier-Stokes equations
+      \begin{equation*}
+         \rho \frac{\partial u_i}{\partial t} + \rho u_k 
+         \frac{\partial u_i}{\partial x_k} = 
+         - \frac{\partial p}{\partial x_i} - \rho \varepsilon_{ijk} 
+         f_j u_k - \frac{\partial \phi}{\partial x_i} + \mu 
+         \left\{ \frac{\partial^2 u_i}{\partial x_k^2} + \frac{1}{3} 
+         \frac{\partial}{\partial x_i} \left( 
+         \frac{\partial u_k}{\partial x_k} \right) \right\}
+      \end{equation*}
+      \item \onslide<3->First principle
+      \begin{equation*}
+         \rho \frac{\partial T}{\partial t} + \rho u_k \frac{\partial T}{\partial x_k} = \mu_\mathrm{h} \frac{\partial^2 T}{\partial x_k^2} + Q
+      \end{equation*}
+      \item \onslide<4->Equation for passive scalar
+      \begin{equation*}
+         \rho \frac{\partial \psi}{\partial t} + \rho u_k \frac{\partial \psi}{\partial x_k} = \mu_{\psi} \frac{\partial^2 \psi}{\partial x_k^2} + Q_{\psi}
+      \end{equation*}
+      \item \onslide<5->Continuity equation
+      \begin{equation*}
+         \frac{\partial p}{\partial t} = - \frac{\partial \rho u_k}{\partial x_k} 
+      \end{equation*}
+   \end{itemize}
+\end{frame}
+
+% Folie 3
+\begin{frame}
+   \frametitle{Boussinesq Approximation}
+   \small
+   \begin{itemize}
+      \item \onslide<2->Splitting thermodynamic variables into a basic state $\psi_0$ and a variation $\psi^{*}$ 
+      \begin{equation*}
+         p(x,y,z,t) = p_0(x,y,z,t) + p^{*}(x,y,z,t)\hspace{22mm}
+      \end{equation*}
+      \begin{equation*}
+         \rho(x,y,z,t) = \rho_0(x,y,z,t) + \rho^{*}(x,y,z,t) ; 
+         \hspace{5mm} \psi^{*} << \psi_0
+      \end{equation*} 
+      \item \onslide<3->Hydrostatic equilibrium, geostrophic wind (not included in Boussinesq)
+      \begin{equation*}
+         \frac{\partial p_0}{\partial z} = -g \rho_0 \hspace{10mm} 
+         \frac{1}{\rho_0} \frac{\partial p_0}{\partial x} = -f v_\mathrm{g}, 
+         \hspace{5mm} \frac{1}{\rho_0} \frac{\partial p_0}{\partial y} = f u_\mathrm{g}
+      \end{equation*}
+      \item \onslide<4->Equation of state
+      \begin{equation*}
+         p_0 = \rho_0 R T_0 \rightarrow \ln{p_0} = \ln{\rho_0} + \ln{R} + \ln{T_0} \rightarrow \frac{\partial p_0}{p_0} = \frac{\partial \rho_0}{\rho_0} + \frac{\partial T_0}{T_0} 
+      \end{equation*}
+      \begin{equation*}
+         \frac{\Delta p_0}{p_0} \approx \frac{\Delta \rho_0}{\rho_0} + 
+         \frac{\Delta T_0}{T_0} \rightarrow \frac{p^{*}}{p_0} \approx 
+         \frac{\rho^{*}}{\rho_0} + \frac{T^{*}}{T_0} \hspace{10mm} 
+         \frac{\rho^{*}}{\rho_0} \approx - \frac{T^{*}}{T_0} \hspace{10mm}
+      \end{equation*}
+   \end{itemize}
+\end{frame}
+
+% Folie 4
+\begin{frame}
+   \frametitle{Continuity Equation}
+   \begin{eqnarray*}
+      \onslide<2-> \dfrac{\partial \rho_0(z)}{\partial t} = 
+      - \dfrac{\partial \rho_0(z) u_k}{\partial x_k} & 
+      \hspace{10mm} \dfrac{\partial \rho_0 u_k}{\partial x_k} = 0 
+      \hspace{5mm} & \text{anelastic approximation}\\
+      \\
+      \onslide<3-> \rho_0 = const. & \hspace{10mm} 
+      \dfrac{\partial u_k}{\partial x_k} = 0 \hspace{5mm} & 
+      \text{incompressible flow}
+   \end{eqnarray*}
+\end{frame}
+
+% Folie 5
+\begin{frame}
+   \frametitle{Boussinesq Approximated Equations}
+   \begin{itemize}
+      \item \onslide<2->Navier-Stokes equations
+      \begin{equation*}
+         \frac{\partial u_i}{\partial t} 
+         + \frac{\partial u_k u_i}{\partial x_k} =  
+         - \frac{1}{\rho_0}\frac{\partial p^{*}}{\partial x_i} 
+         - \varepsilon_{ijk} f_j u_k + \varepsilon_{i3k} f_3 u_{k_\mathrm{g}} 
+         + g \frac{T - T_0}{T_0} \delta_{i3} + \nu 
+         \frac{\partial^2 u_i}{\partial x_k^2}
+      \end{equation*}
+      \item \onslide<3->First principle
+      \begin{equation*}
+         \frac{\partial T}{\partial t} + u_k \frac{\partial T}{\partial x_k} = 
+         \nu_\mathrm{h} \frac{\partial^2 T}{\partial x_k^2} + Q
+      \end{equation*}
+      \item \onslide<4->Equation for passive scalar
+      \begin{equation*}
+         \frac{\partial \psi}{\partial t} + u_k 
+         \frac{\partial \psi}{\partial x_k} = \nu_{\psi} 
+         \frac{\partial^2 \psi}{\partial x_k^2} + Q_{\psi}
+      \end{equation*}
+      \item \onslide<5->Continuity equation
+      \begin{equation*}
+         \frac{\partial u_k}{\partial x_k} = 0
+      \end{equation*}
+   \end{itemize}
+   \onslide<6-> \tikzstyle{plain} = [rectangle, draw, text width=0.27\textwidth, font=\small]
+
+   \begin{tikzpicture}[remember picture, overlay]
+      \node at (current page.north west){%
+      \begin{tikzpicture}[overlay]
+         \node[plain, draw,anchor=west] at (94mm,-55mm) {\noindent This set of equations is valid for almost all kind of CFD models!};
+      \end{tikzpicture}
+      };
+   \end{tikzpicture}
+\end{frame}
+
+
+\section{Scale Separation}
+\subsection{Scale Separation by Spatial Filtering}
+
+% Folie 6
+\begin{frame}
+   \frametitle{LES - Scale Separation by Spatial Filtering (I)}
+   \footnotesize
+   \begin{itemize}
+      \item<1->{LES technique is based on scale separation, in order to reduce the number of degrees of freedom of the solution. \begin{math} \boxed{\Psi(x_i , t) = \overline{\Psi}(x_i , t) + \Psi'(x_i , t)} \end{math}}
+      \item<2->{Large / low-frequency modes $\Psi$ are calculated directly (resolved scales).}
+      \item<3->{Small / high-frequency modes $\Psi'$ are parameterized using a statistical model (subgrid / subfilter scales, SGS model).}
+      \item<4->{These two categories of scales are seperated by defining a cutoff length $\Delta$.}
+   \end{itemize}
+   \normalsize
+   \includegraphics[width=\textwidth]{basic_equations_figures/Spatial_Filtering_I.png}
+\end{frame}
+
+
+
+% Folie 7
+\begin{frame}
+   \frametitle{LES - Scale Separation by Spatial Filtering (II)}
+   \begin{columns}[T]
+      \begin{column}{0.8\textwidth}
+      \footnotesize
+      \begin{itemize}
+         \item<1->The Filter applied is a spatial filter:
+         \begin{equation*} 
+            \overline{\Psi}(x_i) = \int_D G(x_i - x_i') \Psi(x_i')dx_i' 
+         \end{equation*}
+         \begin{equation*} 
+            \overline{\Psi}'(x_i) = 0 \qquad but \qquad \overline{\overline{\Psi}} \neq \overline{\Psi}(x_i) 
+         \end{equation*}  
+         \item<2->Filter applied to the nonlinear advection term:
+         \begin{equation*} 
+            \overline{u_k u_i} = \overline{(\overline{u_k} + u_k')(\overline{u_i} + u_i')} = \overline{\overline{u_k}\,\overline{u_i}} + \underbrace{\overline{\overline{u_k}          u_i'} + \overline{u_k' \overline{u_i}}}_{C_{ki}} + \underbrace{\overline{u_k' u_i'}}_{R_{ki}} 
+         \end{equation*}   
+         \item<5->Leonard proposes a further decomposition:
+         \begin{equation*} 
+            \overline{\overline{u_k}\,\overline{u_i}} = \overline{u_k}\,\overline{u_i} + \underbrace{\left( \overline{\overline{u_k}\,\overline{u_i}} - \overline{u_k}\,\overline{u_i} \right)}_{L_{ki}}                         
+         \end{equation*}
+         \begin{equation*} 
+            \overline{u_k u_i} = \overline{u_k}\,\overline{u_i} + L_{ki} + C_{ki} + R_{ki} = \overline{u_k}\,\overline{u_i} + \tau_{ki} 
+         \end{equation*}       
+      \end{itemize}
+      \end{column}
+      \begin{column}{0.32\textwidth}
+      \vspace{45mm}     
+      \begin{footnotesize}
+         \onslide<3->$R_{ki}$: \textbf{Reynolds-stress} \\
+         $C_{ki}$: \textbf{cross-stress} \\
+         $L_{ki}$: \textbf{Leonard-stress} \\
+         $\tau_{ki}$: \textbf{total stress-tensor}
+      \end{footnotesize}
+      \end{column}
+   \end{columns}
+   \onslide<4->\tikzstyle{plain} = [rectangle, draw, text width=0.27\textwidth, font=\small]
+      \begin{tikzpicture}[remember picture, overlay]
+      \node at (current page.north west){
+      \begin{tikzpicture}[overlay]
+         \node[plain, draw,anchor=west] at (94mm,-30mm) {
+         \begin{footnotesize}
+            \noindent \textbf{Ensemble average:} \\
+         \end{footnotesize}
+         $\overline{\overline{\Psi}}(x_i) = \overline{\Psi}(x_i)$\\
+         \vspace{5mm}
+         $\overline{u_k u_i} = \overline{u_k}\,\overline{u_i} + \overline{u_k' u_i'}$
+         };
+      \end{tikzpicture}
+      };
+   \end{tikzpicture}   
+\end{frame}
+
+% Folie 8
+\begin{frame}
+   \frametitle{LES - Scale Separation by Spatial Filtering (III)}
+   \small
+   \begin{itemize}
+      \item<2-> Volume-balance approach (Schumann, 1975)\\ advantage: numerical discretization acts as a\\ Reynolds operator
+      \begin{flalign*}
+         &\Psi(V,t)=\frac{1}{\Delta x \cdot \Delta y \cdot \Delta z} = \int \int \int_V \Psi(V',t) dV'&\\
+         &\overline{\Psi'}(x_i)=0 \hspace{5mm} \text{and} \hspace{5mm} \overline{\overline{\Psi}} = \overline{\Psi}\\
+         &V=\left[ x - \frac{\Delta x}{2}, x + \frac{\Delta x}{2} \right] \times \left[ y - \frac{\Delta y}{2}, y + \frac{\Delta y}{2} \right] \times \left[ z - \frac{\Delta z}{2}, z + \frac{\Delta z}{2} \right]
+      \end{flalign*}
+      \item<3-> Filter applied to the nonlinear advection term:
+      \begin{equation*}
+         \overline{u_k u_i} = \overline{(\overline{u_k}+u'_k)(\overline{u_i}+u'_i)}=
+         \overline{u_k}\,\overline{u_i}+\overline{u'_k u'_i}
+      \end{equation*}
+   \end{itemize}
+   \onslide<1->\tikzstyle{plain} = [rectangle, draw, text width=0.27\textwidth, font=\small]
+      \begin{tikzpicture}[remember picture, overlay]
+      \node at (current page.north west){
+      \begin{tikzpicture}[overlay]
+         \node[plain, draw,anchor=west] at (94mm,-30mm) {
+         \begin{footnotesize}
+            \noindent \textbf{Ensemble average:} \\
+         \end{footnotesize}
+         $\overline{\overline{\Psi}}(x_i) = \overline{\Psi}(x_i)$\\
+         \vspace{5mm}
+         $\overline{u_k u_i} = \overline{u_k}\,\overline{u_i} + \overline{u_k' u_i'}$
+         };
+      \end{tikzpicture}
+      };
+   \end{tikzpicture}
+ \end{frame}
+
+
+\section{Filtered equations}
+\subsection{The Filtered Equations}
+
+% Folie 9
+\begin{frame}
+   \frametitle{The Filtered Equations}
+   \onslide<2->
+   \begin{equation*}
+      \frac{\partial \overline{u_i}}{\partial t} 
+      + \frac{\partial \overline{u_k}\,\overline{u_i}}{\partial x_k} = 
+      - \frac{1}{\rho_0} \frac{\partial \overline{p}^*}{\partial x_i} 
+      - \varepsilon_{ijk}f_j \overline{u_k} + \varepsilon_{i3k} f_3 \overline{u}_{k_\mathrm{g}} 
+      + g \frac{\overline{T}-T_0}{T_0} \delta_{i3} 
+      + \nu \frac{\partial^2 \overline{u_i}}{\partial x_k^2} 
+      - \frac{\partial \tau_{ki}}{\partial x_k}
+   \end{equation*}
+
+   \begin{footnotesize}
+      \begin{itemize}
+         \item<3->The previous derivation completely ignores the existance of the computational grid.
+         \item<4->The computational grid introduces another space scale: the discretization step $\Delta x_i$.
+         \item<5->$\Delta x_i$ has to be small enough to be able to apply the filtering process correctly: $\Delta x_i \le \Delta$
+         \item<6-> Two possibilities:\\
+         1. Pre-filtering technique\\
+         ($\Delta x < \Delta$,  explicit filtering)\\
+         2. Linking the analytical filter\\
+         to the computational grid\\
+         ($\Delta x = \Delta$, implicit filtering)
+      \end{itemize}
+   \end{footnotesize}
+
+   \begin{picture}(0.0,0.0) 
+      \put(140,13){\uncover<6->{\includegraphics[width=0.6\textwidth]{basic_equations_figures/explicit_implicit.png}}}
+   \end{picture}
+\end{frame}
+
+%% Folie 10
+\begin{frame}
+  \frametitle{Explicit Versus Implicit Filtering}
+   \begin{itemize}
+      \item<2-> Explicit filtering:
+      \begin{itemize}
+         \small
+         \item<2-> Requires that the analytical filter is applied explicitly.
+         \item<3-> Rarely used in practice, due to additional computational costs.
+      \end{itemize}
+      \item<4-> Implicit filtering:
+      \begin{itemize}
+         \small
+         \item<4-> The analytical cutoff length is associated with the grid spacing.
+         \item<5-> This method does not require the use of an analytical filter.
+         \item<6-> The filter characteristic cannot really be controlled.
+         \item<7-> Because of its simplicity, this method is used by nearly all LES models.
+      \end{itemize}
+   \end{itemize}
+
+   \onslide<8->
+   \begin{scriptsize}
+      \textbf{Literature:}\\
+      \textbf{Sagaut, P., 2001:} Large eddy simulation for incompressible flows: An introduction. Springer Verlag, Berlin/Heidelberg/New York, 319 pp.\\
+      \textbf{Schumann, U., 1975:} Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys., \textbf{18}, 376-404.
+   \end{scriptsize}
+\end{frame}
+
+% Folie 11
+\begin{frame}
+   \frametitle{The Final Set of Equations (PALM)}
+   \footnotesize
+   \begin{itemize}
+      \item<2-> Navier-Stokes equations:
+      \onslide<2->
+      \begin{flalign*}
+         &\frac{\partial \overline{u_i}}{\partial t} = - \frac{\partial \overline{u_k}\,\overline{u_i}}{\partial x_k} - \frac{1}{\rho_0} \frac{\partial \overline{\pi}^*}{\partial x_i} - \varepsilon_{ijk}f_j \overline{u_k} + \varepsilon_{i3k} f_3 \overline{u}_{k_\mathrm{g}} + g \frac{\overline{T}-T_0}{T_0} \delta_{i3} + \nu \frac{\partial^2 \overline{u_i}}{\partial x_k^2} - \frac{\partial \tau_{ki}^r}{\partial x_k}&
+      \end{flalign*}
+      \item<4-> First principle (using potential\\ temperature):
+      \onslide<4->
+      \begin{flalign*}
+         &\frac{\partial \overline{\theta}}{\partial t} = - \frac{\partial \overline{u_k}\,\overline{\theta}}{\partial x_k} - \frac{\partial H_k}{\partial x_k} + Q_{\theta}&
+      \end{flalign*}
+      \item<5-> Equation for specific humidity\\ (passive scalar)
+      \onslide<5->
+      \begin{flalign*}
+         &\frac{\partial \overline{\theta}}{\partial t} = - \frac{\partial \overline{u_k}\,\overline{\theta}}{\partial x_k} - \frac{\partial H_k}{\partial x_k} + Q_{\theta}&
+      \end{flalign*}
+      \item<6-> 
+      Continuity equation
+      \onslide<6->
+      \begin{flalign*}
+         &\frac{\partial \overline{u_k}}{\partial x_k} = 0&
+      \end{flalign*}
+   \end{itemize}
+
+   \onslide<3->\tikzstyle{plain} = [rectangle, draw, text width=0.40\textwidth, font=\small]
+   \begin{tikzpicture}[remember picture, overlay]
+      \node at (current page.north west){
+      \begin{tikzpicture}[overlay]
+         \node[plain, draw,anchor=west] at (75mm,-45mm) {
+         \begin{tiny}
+            \noindent normal stresses included in the stress tensor are now included in a modified dynamic pressure:\\
+         \end{tiny}
+         $\tau_{ki}^r = \tau_{ki} - \frac{1}{3} \tau_{jj} \delta_{ki}$\\
+         \vspace{1mm}
+         $\overline{\pi}^* = \overline{p}^* + \frac{1}{3} \tau_{jj} \delta_{ki}$
+         };
+      \end{tikzpicture}
+      };
+   \end{tikzpicture}
+
+   \onslide<7->\tikzstyle{plain} = [rectangle, draw, text width=0.40\textwidth, font=\small]
+   \begin{tikzpicture}[remember picture, overlay]
+      \node at (current page.north west){
+      \begin{tikzpicture}[overlay]
+         \node[plain, draw,anchor=west] at (75mm,-70mm) {
+         \begin{tiny}
+            \noindent subgrid-scale stresses (fluxes) to be parameterized in the SGS model:\\
+         \end{tiny}
+         $\tau_{ki} = \overline{u_k u_i} - \overline{u_k}\,\overline{u_i}$\\
+         $H_{k} = \overline{u_k \theta_k} - \overline{u_k}\,\overline{\theta_i}$\\
+         $W_{k} = \overline{u_k q_k} - \overline{u_k}\,\overline{q_k}$
+         };
+      \end{tikzpicture}
+      };
+   \end{tikzpicture}
+\end{frame}
+
+
+\end{document}
Index: palm/trunk/TUTORIAL/SOURCE/fundamentals_of_les.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/fundamentals_of_les.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/fundamentals_of_les.tex	(revision 915)
@@ -0,0 +1,274 @@
+% $Id$
+\input{header_tmp.tex}
+%\input{../header_lectures.tex}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{pgf}
+\usetheme{Dresden}
+\usepackage{subfigure}
+\usepackage{units}
+\usepackage{multimedia}
+\usepackage{hyperref}
+\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
+\usepackage{xmpmulti}
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows,positioning}
+\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+
+%---------- neue Pakete
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{multicol}
+
+\institute{Institut fÃŒr Meteorologie und Klimatologie, Leibniz UniversitÃ€t Hannover}
+\date{last update: \today}
+\event{PALM Seminar}
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamertemplate{footline}
+  {%
+    \begin{beamercolorbox}[rightskip=-0.1cm]&
+     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
+      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
+      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
+    \end{beamercolorbox}%
+%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
+%    \end{beamercolorbox}
+  }%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.eps}}
+
+\title[Fundamentals of Large-Eddy Simulation]{Fundamentals of Large-Eddy Simulation}
+\author{Siegfried Raasch}
+
+% Notes:
+% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
+% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
+\begin{document}
+%Folie 1
+\begin{frame}
+\titlepage
+\pdfnote{maronga}{Welcome to the PALM Tutorial!}
+\end{frame}
+
+\section{The Role of Turbulence}
+\subsection{The Role of Turbulence}
+
+% Folie 2
+\begin{frame}
+   \frametitle{The Role of Turbulence (I)}
+   \begin{itemize}
+      \item<1->{\textbf{Most flows in nature \& technical applications are turbulent}}
+      \item<2->{\textbf{Significance of Turbulence}}
+      \begin{itemize}
+         \item<2->{\underline{Meteorology / Oceanography:} Transport processes of momentum, heat, water vapor as well as other scalars}
+         \item<2->{\underline{Health care:} Air pollution}
+         \item<2->{\underline{Aviation, Engineering:} Wind impact on buildings, power output of windfarms}
+      \end{itemize}
+      \item<3->{\textbf{Characteristics of turbulence}}
+      \begin{itemize}
+         \item<3->{non-periodical, 3D stochastic movements}
+         \item<3->{mixes air and its properties on scales between large-scale advection and molecular diffusion}
+         \item<3->{non-linear $\rightarrow$ energy is distributed smoothly with wavelength}
+         \item<3->{wide range of spatial and temporal scales}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 3
+\begin{frame}
+   \frametitle{The Role of Turbulence (II)}
+   \begin{columns}[c]
+   \column{0.5\textwidth}
+      \scriptsize
+      \begin{itemize}
+         \item<2->{\textbf{Large eddies:} $\unit[10^3]{m}$ ($L$), $\unit[1]{h}$ \\
+                   \textbf{Small eddies:} $\unit[10^{-3}]{m}$ ($\eta$), \unit[0.1]{s}}
+         \item<3->{\textbf{Energy production and dissipation on different scales}}
+         \begin{itemize}
+            \item<3->{\begin{scriptsize} Large scales: shear and buoyant production \end{scriptsize}}
+            \item<3->{\begin{scriptsize} Small scales: viscous dissipation \end{scriptsize}}
+         \end{itemize}
+         \item<4->{\textbf{Large eddies contain most energy}}
+         \item<5->{\textbf{Energy-cascade} \\ 
+                   Large eddies are broken up by instabilities and their energy is handled down to smaller scales.}
+      \end{itemize}
+      \normalsize
+   \column{0.5\textwidth}
+      \onslide<3->{
+         \includegraphics[width=\textwidth, height=0.9\textheight]{fundamentals_of_les_figures/Role_of_Turbulence_2.png}}
+   \end{columns}
+\end{frame}
+
+\section{The Reynolds Number}
+\subsection{The Reynolds Number}
+
+% Folie 4
+\begin{frame}
+   \frametitle{The Reynolds Number (Re)}
+   \begin{columns}[c]
+   \column{0.6\textwidth}
+      \onslide<1->{
+         $\frac{L}{\eta} \approx Re^{3/4} \approx 10^6$ \quad \begin{small} (in the atmosphere) \end{small}}
+      \par\bigskip
+      \onslide<2->{
+         $Re = \frac{\left| \textbf{u} \cdot \nabla \textbf{u} \right|}{\left| \nu \nabla^2 \textbf{u} \right|} \hat{=} \frac{LU}{\nu} \qquad \frac{\textnormal{inertia forces}}{\textnormal{viscous forces}} $}
+   \column{0.4\textwidth}
+      \footnotesize
+      \onslide<1->{
+         \textbf{u} 3D wind vector
+
+         $\nu$ kinematic molecular viscosity 
+
+         $L$ outer scale of turbulence
+
+         $U$ characteristic velocity scale
+
+         $\eta$ inner scale of turbulence
+            \begin{scriptsize}(Kolmogorov dissipation length) \end{scriptsize} }             
+   \end{columns}
+   \normalsize
+   \par\bigskip
+   \par\bigskip
+   \onslide<3->{
+      $ \Rightarrow $ \underline{Number of gridpoints for a 3D simulation:}
+   \par\bigskip
+   $ \left( \frac{L}{\eta} \right)^3 \approx Re^{9/4} \approx 10^{18}$ (in the atmosphere)}
+\end{frame}
+
+\section{Classes of Turbulence Models}
+\subsection{Classes of Turbulence Models}
+
+% Folie 5
+\begin{frame}
+   \frametitle{Classes of Turbulence Models (I)}
+   \begin{itemize}
+      \item{\textbf{Direct numerical Simulation (DNS)}}
+      \begin{itemize}
+         \item<2->{\textbf{Most straight-forward approach:}}
+         \begin{itemize}
+            \item<2->{Resolve all scales of turbulent flow explicitly.}
+         \end{itemize}
+         \item<3->{\textbf{Advantage:}}
+         \begin{itemize}
+            \item<3->{(In principle) a very accurate turbulence representation.}
+         \end{itemize}
+         \item<4->{\textbf{Problem:}}
+         \begin{itemize}
+            \item<4->{Limited computer resources  (1996: $\sim$ $10^8$, today: $\sim$ $10^{11}$ gridpoints, 
+                      but $\sim$ $10^{18}$ gridpoints needed, see prior slide).}
+            \item<4->{$\unit[1]{h}$ simulation of $10^9$ ($2048^3$) gridpoints on $512$ processors of the HLRN supercomputer needs $\unit[10]{h}$ CPU time.}
+         \end{itemize}
+         \item<5->{\textbf{Consequences:}}
+         \begin{itemize}
+            \item<5->{DNS is restricted to moderately turbulent flows (low Reynolds-number flows).}
+            \item<5->{Highly turbulent atmospheric turbulent flows cannot be simulated.}
+         \end{itemize}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 6
+\begin{frame}
+   \frametitle{Classes of Turbulence Models (II)}
+   \begin{itemize}
+      \item{\textbf{Reynolds averaged (Navier-Stokes) simulation (RANS)}}
+      \begin{itemize}
+         \item<2->{\textbf{Opposite strategy:}}
+         \begin{itemize}
+            \item<2->{Applications that only require average statistics of the flow (i.e. the mean flow).}
+            \item<2->{Integrate merely the ensemble-averaged equations.}
+            \item<2->{Parameterize turbulence over the whole eddy spectrum.}
+         \end{itemize}
+         \item<3->{\textbf{Advantage:}}
+         \begin{itemize}
+            \item<3->{Computationally inexpensive, fast.}
+         \end{itemize}
+         \item<4->{\textbf{Problem:}}
+         \begin{itemize}
+            \item<4->{Turbulent fluctuations not explicitly captured.}
+            \item<4->{Parameterizations are very sensitive to large-eddy structure that depends on 
+                      environmental conditions such as geometry and stratification $\rightarrow$     
+                      Parameterizations are not valid for a wide range of different flows.}
+         \end{itemize}
+         \item<5->{\textbf{Consequence:}}
+         \begin{itemize}
+            \item<5->{Not suitable for detailed turbulence studies.}
+         \end{itemize}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 7
+\begin{frame}
+   \frametitle{Classes of Turbulence Models (III)} 
+   \begin{itemize}
+      \item{\textbf{Large eddy simulation (LES)}}
+      \begin{itemize}
+         \item<2->{Seeks to combine advantages and avoid disadvantages of DNS and RANS by \underline{treating 
+                   large scales and small scales separately}, based on Kolmogorov's (1941) similarity theory of turbulence.}
+         \item<3->{Large eddies are explicitly resolved.}
+         \item<4->{The impact of small eddies on the large-scale flow is parameterized.}
+         \item<5->{Advantages:}
+         \begin{itemize}
+            \item<5->{Highly turbulent flows can be simulated.}
+            \item<5->{Local homogeneity and isotropy at large \textit{Re} (Kolmogorov's $1^\mathrm{st}$ hypothesis) leaves 
+                      parameterizations uniformly valid for a wide range of different flows.}
+         \end{itemize}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+\section{Concept of LES}
+\subsection{Concept of LES}
+
+ % Folie 8
+ \begin{frame}
+    \frametitle{Concept of Large Eddy Simulation (I)}
+    \begin{columns}
+       \column{0.55\textwidth}
+          \begin{itemize}
+             \item<1->{\textbf{Filtering}}
+             \begin{footnotesize}
+                \begin{itemize}
+                   \item<2->{Spectral cut at wavelength $\Delta x$.}
+                   \item<3->{Structures larger than $\Delta x$ are explicitly calculated (resolved scales).}
+                   \item<4->{Structures smaller than $\Delta x$ must be filtered out (subgrid scales), formally known as low-pass filtering.}
+                   \item<5->{Like for Reynolds averaging: split variables in mean part and fluctuation, spatially average the model equations, e.g.:}
+                \end{itemize}
+             \end{footnotesize}
+             \onslide<6->{\begin{center} $w = \overline{w} + w', \theta = \overline{\theta} + \theta'$ \end{center}}
+          \end{itemize}
+       \column{0.45\textwidth}
+          \includegraphics[width=\textwidth]{fundamentals_of_les_figures/Concept_of_LES.png}
+    \end{columns}
+ \end{frame}
+
+% Folie 9
+\begin{frame}
+   \frametitle{Concept of Large Eddy Simulation (II)}
+   \begin{itemize}
+      \item<1->{\textbf{Parameterization}}   
+      \begin{footnotesize}
+      \begin{itemize}
+         \item<2->{The filter procedure removes the small scales from the model equations, but it produces new unknowns, mainly averages of fluctuation products.}
+         \begin{itemize} 
+            \item<2->{eg. $\overline{w'\theta'}$}
+         \end{itemize}
+         \item<3->{These unknowns describe the effect of the unresolved, small scales on the resolved, large scales; therefore it is important to include them in the model.}
+         \item<4->{We do not have information about the variables (e.g., vertical wind component and potential temperature) on these small scales of their fluctuations.}
+         \item<5->{Therefore, these unknowns have to be parameterized using information from the resolved scales.}
+         \begin{itemize}
+            \item<5->{A typical example is the flux-gradient relationship, e.g.,}
+         \end{itemize}
+      \end{itemize}
+      \end{footnotesize}
+   \end{itemize}
+   \onslide<5->{
+      \begin{center}
+      $ \overline{w'\theta'} = - \nu_\mathrm{h} \cdot \frac{\partial \overline{\theta}}{\partial z} $ 
+      \end{center}}
+\end{frame}
+
+\end{document}
Index: palm/trunk/TUTORIAL/SOURCE/handoutWithNotes.sty
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/handoutWithNotes.sty	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/handoutWithNotes.sty	(revision 915)
@@ -0,0 +1,466 @@
+% Copyright 2009 by Guido Diepen <guido@guidodiepen.nl>
+% 	Parts provided by Edson Valle
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+% 
+% Changelog
+%	20091202 - Added "1 on 1 with notes" layout, provided by Harald Welte
+%	20091108 - Added "2 on 1 with notes landscape" layout, provided by Edson Valle
+%	20091104 - Added "3 on 1 with notes" layout
+%	20091104 - Added "2 on 1 with notes" layout
+%	20091104 - Added "1 on 1 with notes landscape" layout, provided by Edson Valle
+%   20090101 - Initial Version
+
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+    %\hrule width\paperwidth\vskip1cm
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+    \hrule width\paperwidth\vskip1cm
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+
+
Index: palm/trunk/TUTORIAL/SOURCE/header_HANDOUT.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/header_HANDOUT.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/header_HANDOUT.tex	(revision 915)
@@ -0,0 +1,8 @@
+% $Id$
+%Create handouts (copies for students)
+\documentclass[handout]{beamer}
+\usepackage{../handoutWithNotes}
+\pgfpagesuselayout{2 on 1 with notes landscape}[a4paper]
+
+\newcommand{\pdfnote}[2]{}
+\newcommand{\pdfwarn}[2]{}
Index: palm/trunk/TUTORIAL/SOURCE/header_LECTURE.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/header_LECTURE.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/header_LECTURE.tex	(revision 915)
@@ -0,0 +1,7 @@
+% $Id$
+% Create presentation with transitions (lectures)
+\documentclass{beamer}
+\usepackage[final,author={Siegfried Raasch}]{pdfcomment}
+
+\newcommand{\pdfnote}[2]{}
+\newcommand{\pdfwarn}[2]{}
Index: palm/trunk/TUTORIAL/SOURCE/header_WEB.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/header_WEB.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/header_WEB.tex	(revision 915)
@@ -0,0 +1,30 @@
+% $Id$
+% Create presentation with comments (no transitions) (trac-system)
+\documentclass[handout]{beamer}
+\usepackage[author=raasch]{pdfcomment}
+
+
+\definestyle{note}{icon=Comment,color=white,open=true}
+\definestyle{warning}{icon=Comment,color=red,open=true}
+
+\newcounter{slidenum}
+
+\newcommand{\pdfnote}[2]{%
+\setcounter{slidenum}{\insertpagenumber}
+\addtocounter{slidenum}{1}
+\addtocounter{slidenum}{-\insertframestartpage}
+%\arabic{slidenum}
+%\arabic{beamerpauses}
+\only<\value{beamerpauses}>{\pdfcomment[style=note,author=#1]{#2}}%
+% \onslide*<\value{slidenum}>{\pdfcomment[style=note,author=#1]{#2}}%
+}
+
+\newcommand{\pdfwarn}[2]{%
+\setcounter{slidenum}{\insertpagenumber}
+\addtocounter{slidenum}{1}
+\addtocounter{slidenum}{-\insertframestartpage}
+%\arabic{slidenum}
+%\arabic{beamerpauses}
+\only<\value{beamerpauses}>{\pdfcomment[style=warning,author=#1]{#2}}%
+% \onslide*<\value{slidenum}>{\pdfcomment[style=note,author=#1]{#2}}%
+}
Index: palm/trunk/TUTORIAL/SOURCE/non_cyclic_boundary_conditions.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/non_cyclic_boundary_conditions.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/non_cyclic_boundary_conditions.tex	(revision 915)
@@ -0,0 +1,363 @@
+% $Id$
+\input{header_tmp.tex}
+%\input{header_lectures.tex}
+
+\usepackage[utf8]{inputenc}
+\usepackage{ngerman}
+\usepackage{pgf}
+\usetheme{Dresden}
+\usepackage{subfigure}
+\usepackage{units}
+\usepackage{multimedia}
+\usepackage{hyperref}
+\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
+\usepackage{xmpmulti}
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows,positioning}
+\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+
+%---------- neue Pakete
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{multicol}
+\usepackage{pdfcomment}
+
+\institute{Institut fÃŒr Meteorologie und Klimatologie, Leibniz UniversitÃ€t Hannover}
+\date{last update: \today}
+\event{PALM Seminar}
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamertemplate{footline}
+  {%
+    \begin{beamercolorbox}[rightskip=-0.1cm]&
+     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
+      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
+      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
+    \end{beamercolorbox}%
+%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
+%    \end{beamercolorbox}
+  }%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.eps}}
+
+\title[PALM - Using Non-Cyclic Boundary Conditions]{PALM - Using Non-Cyclic Boundary Conditions}
+\author{Siegfried Raasch}
+
+% Notes:
+% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
+% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
+\begin{document}
+
+% Folie 1
+\begin{frame}
+\titlepage
+\end{frame}
+
+% Folie 2
+\begin{frame}
+   \frametitle{Cyclic Horizontal Boundary Conditions}
+   In many cases, LES models are using cyclic horizontal boundary conditions.
+   \par\bigskip
+   \textbf{Why?}
+   \par\bigskip
+   \begin{itemize}
+      \item<2->{LES requires that the main energy containing eddies are resolved by the model.}
+      \item<3->{With cyclic boundary conditions, turbulence can freely develop and is not effected by the side walls (because there are no walls!).}
+      \item<4->{Non-cyclic boundary conditions give problems:}
+      \begin{itemize}
+         \item<5->{If Dirichlet conditions (fixed vertical profiles) are used at the inflow, the inflow is laminar and some (significant) domain space is needed in order to develop                         turbulence.}
+         \item<6->{At the outflow, a boundary condition is required which allows the eddies to freely leave the domain.}
+      \end{itemize}
+   \end{itemize}   
+\end{frame}
+
+%Folie 3
+\begin{frame}
+   \frametitle{Motivation for Non-Cyclic Boundary Conditions}
+   \footnotesize
+   The main motivation for non-cyclic boundary conditions are studies of isolated phenomena.
+   \begin{tabbing}
+   \uncover<2->{\textbf{Example:} \= Turbulence generated by a single obstacle. \\}                    
+                    \uncover<6->{ \> Cyclic boundary conditions along x would allow the generated turbulence\\
+                     \>  to enter the domain again, and so finally to modify the turbulence \\
+                     \>  on the leeward side of the building. \\ }      
+                     \\ 
+                     \uncover<9>{ \> This wouldn't be a simulation of a single building, but of an\\
+                     \> infinite row of buildings! \\  }
+   \end{tabbing}
+   \begin{center}
+   \includegraphics<3>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_1.png}
+   \includegraphics<4>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_2.png}
+   \includegraphics<5-6>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_3.png}
+   \includegraphics<7>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_4.png}
+   \uncover<8->{\begin{center} \includegraphics[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_5.png} \end{center}}
+   \end{center}
+   \normalsize
+\end{frame}
+
+% Folie 4
+\begin{frame}
+   \frametitle{Implications of Non-Cyclic Boundary Conditions}
+   \footnotesize
+   \onslide<2->{Using Dirichlet-conditions (e.g u(z) = const.), there is no turbulence at the inflow. $\rightarrow $the flow is laminar $\rightarrow$ LES approach fails!}
+   \par\bigskip
+   \includegraphics<3>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_1.png}
+   \includegraphics<4>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_2.png}
+   \uncover<5->{\includegraphics[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_3.png}}
+   \par\bigskip
+   \onslide<6->{Flow internal turbulence may develop, but this may require a very long model domain.}
+   \par\bigskip
+   \includegraphics<7>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_4.png}
+   \includegraphics<8>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_5.png}
+   \uncover<9->{\includegraphics[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_6.png}}
+   \onslide<10->{There is a need to supply turbulence information at the inflow.}
+\end{frame}
+
+% Folie 5
+\begin{frame}
+   \frametitle{How to Create a Turbulent Inflow (I)}
+   Two methods:
+   \begin{itemize}
+      \item<2->{by a statistical model}
+      \item<3->{by recycling-method  (Lund et al., 1998)}
+   \end{itemize}
+   \includegraphics<4>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_1_neu.png}
+   \includegraphics<5>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_2_neu.png}
+   \includegraphics<6>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_3_neu.png}
+   \includegraphics<7>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_4_neu.png}
+   \includegraphics<8>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_5_neu.png}
+   \uncover<9->{\includegraphics[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_6.png}}
+   \par\bigskip
+   \uncover<10>{How do we get the initial turbulence in the recycle area? \\
+   If there is no turbulence, there is nothing to recycle!}
+\end{frame}
+
+%Folie 6
+\begin{frame}
+   \frametitle{How to Create a Turbulent Inflow (II)}
+   \small
+   Initial  turbulence is created by a precursor run with cyclic boundary conditions and much smaller domain size than used for the main run.
+   \tikzstyle{line} = [draw, yellow, thick, dashed, -latex']    
+   \begin{tikzpicture}      
+      \uncover<1>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_1.png}};}
+      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_2.png}};}
+      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_3.png}};}
+      \node(text) [right=0.1cm of picture]{
+         \parbox{5cm}{
+         \scriptsize
+         \begin{itemize}
+         \item<4->{When the precursor run is finished, data of the last timestep are stored on disc.}
+         \item<5->{These data are then read by the main run and repeatedly mapped to the main run domain, unless it is completely filled.}
+         \end{itemize}}};
+     \uncover<6>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.9\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_4.png}};}
+     \uncover<7>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.9\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_5.png}};}
+     \uncover<8>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.9\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_6.png}};}
+     \uncover<9>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.9\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_7.png}};}  
+     \uncover<10>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.9\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_8.png}};} 
+     \uncover<11>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.9\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_9.png}};} 
+    \path<7->[line] (-0.45,-1) -- (-0.7,-2.6);
+    \path<7->[line] (1.78,-1) -- (1.68,-2.6);  
+    \path<8->[line] (-0.45,-1) -- (1.68,-2.6);
+    \path<8->[line] (1.78,-1) -- (4,-2.6);
+    \path<9->[line] (-0.45,-1) -- (4,-2.6);
+    \path<9->[line] (1.78,-1) -- (6.4,-2.6);
+    \path<10->[line] (-0.45,-1) -- (6.4,-2.6);
+    \path<10->[line] (1.78,-1) -- (6.9,-2.6);
+   \end{tikzpicture} 
+\end{frame}
+
+% Folie 7
+\begin{frame}
+   \frametitle{How to Create a Turbulent Inflow (III)}
+   \footnotesize
+   \begin{itemize}
+      \item{Inflow profiles for the main run have to be taken from the precursor run. It is recommended to use the horizontally averaged profiles from 
+            the last time step of the precursor run.}
+   \end{itemize}
+   \tikzstyle{line1} = [draw, red, thick, -latex'] 
+   \tikzstyle{line2} = [draw, red, thick, -] 
+   \begin{tikzpicture}
+      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_1.png}};}
+      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_2.png}};}
+      \node(text) [right=0.1cm of picture]{
+         \parbox{6.5cm}{
+         \scriptsize
+         \begin{itemize}
+         \item<6->{Since the height of the turbulent boundary layer may increase with increasing distance from the inflow boundary, recycling has 
+               to be limited to the height of the turbulent boundary layer at the inflow. Otherwise, the boundary layer height will continuously increase with time.}
+         \end{itemize}}};
+   \uncover<4>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.8\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_3.png}};}
+   \uncover<5-6>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.8\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_4.png}};}
+   \uncover<7>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.8\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_5.png}};}
+   \uncover<8>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.8\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_6.png}};}
+   \uncover<9>{\node(picture2) [below=1.8cm of picture.east] {\includegraphics[width=0.8\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_7.png}};}
+      
+   \path<5->[line2] (picture.east) -- (2.25,-1.3);
+   \path<5->[line2] (2.25,-1.3)    -- (-1.2,-1.3);
+   \path<5->[line2] (-1.2,-1.3)    -- (-1.2,-3.2);
+   \path<5->[line1] (-1.2,-3.2)      -- (-0.8,-3.2);
+   \end{tikzpicture}
+\end{frame}
+
+% Folie 8
+\begin{frame}
+   \frametitle{Non-Cyclic Boundary Conditions in PALM (I)}
+   \textbf{Status of availability:}
+   \begin{itemize}
+      \item<2->{Non-cyclic boundary conditions along \textbf{one} of the horizontal directions (x \textbf{or} y).}
+      \begin{itemize}
+         \item<3->{Dirichlet conditions at inflow (stationary vertical profiles, u(z), v(z), pt(z), q(z), w=0).}
+         \item<4->{Radiation conditions at outflow. Tendencies at the boundary are replaced by e.g.}
+      \end{itemize}      
+      \uncover<4->{\begin{math} \frac{\partial u}{\partial t} = -\left(c_g + u\right) \frac{\partial u}{\partial x} = -u^* \frac{\partial u}{\partial x} 
+                     \qquad \textnormal with \qquad u^* = \frac{\Delta x}{\Delta t} \frac{u_{b-1}^t - u_{b-1}^{t-1}}{u_{b-1}^{t-1} - u_{b-2}^{t-1}} \end{math}}
+      \par\bigskip
+      \item<5->{Turbulence recycling method for inflow \textbf{from left}.}
+   \end{itemize}  
+\end{frame}
+
+% Folie 9
+\begin{frame}
+   \frametitle{Non-Cyclic Boundary Conditions in PALM (II)}
+   \par\bigskip
+   \small
+   \textbf{Further requirements for PALM runs using non-cyclic boundary conditions:}
+   \par\bigskip
+   \begin{itemize}
+      \item<2->{The \textbf{multigrid-method} has to be used for solving the Poisson-equation.}
+      \item<3->{A \textbf{damping zone} has sometimes to be activated in the vicinity of the outflow in order to avoid reflection of outgoing gravity waves.}
+      \item<4->{\textbf{Volume flow conservation} should be activated, because otherwise flow acceleration or deceleration may occur along the non-cyclic direction.}
+      \item<5->{If turbulence recycling is not used, it may be neccessary to \textbf{continuously impose perturbations} on the horizontal velocity field in the vicinity of the
+                inflow throughout the whole run, in order to maintain a turbulent state of the flow.}
+   \end{itemize}
+   \normalsize
+\end{frame}
+
+% Folie 10
+\begin{frame}
+   \frametitle{Current Applications of Non-Cyclic BCs (I)}
+   \textbf{Cold air outbreaks}
+   \par\bigskip
+   \includegraphics[width=\textwidth]{non_cyclic_figures/cold_air_outbreaks.png} \\
+   \par\bigskip
+   \tiny
+   \textbf{Gryschka, M., C. Dr\"ue, D. Etling and S. Raasch. 2008}: On the influence of sea-ice inhomogeneities onto roll convection in cold-air outbreaks. Geophys. Res. Lett.,
+   \textbf{35}, L23804, doi:10.1029/2008GL035845. \\
+   \par\bigskip
+   \textbf{Gryschka, M. and S. Raasch, 2005}: Roll Convection During a Cold Air Outbreak: A Large Eddy Simulation with Stationary Model Domain. Geophys. Res. Lett., \textbf{32}, L14805,
+    doi:10.1029/2005GL022872. \\
+   \normalsize
+   \begin{center} \uncover<2->{\textbf{Turbulence recycling has not been used!}} \end{center}
+\end{frame}
+
+% Folie 11
+\begin{frame}
+   \frametitle{Current Applications of Non-Cyclic BCs (II)}
+   \textbf{Cold air outbreaks}
+   \begin{center}  
+   \includegraphics[width=0.85\textwidth]{non_cyclic_figures/cold_air_outbreaks_2.png} \\
+   liquid water content (vertically intgrated)  
+   \end{center}
+\end{frame}
+
+% Folie 12
+\begin{frame}
+   \frametitle{How to set up non-cyclic runs with PALM}
+   \begin{itemize}
+      \item{\textbf{required} / recommended parameter settings:}
+   \end{itemize}
+   \par\bigskip
+   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
+   \begin{tikzpicture}      
+      \node[box](inipar){ \begin{tabbing} 
+         \&inipar \= ....... \\
+                  \\
+                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, (bc\_ns = 'dirichlet/radiation',) \\ 
+                  \> \textbf{psolver = 'multigrid'}, \\
+                  \\
+                  \> initializing\_actions = 'set\_1d-model\_profiles', \\
+                  \> conserve\_volume\_flow = .T., \\
+                  \\
+                  \> ...... / \\ \end{tabbing}};
+   \end{tikzpicture}
+\end{frame}
+
+% Folie 13
+\begin{frame}
+   \frametitle{How to set up turbulence recycling with PALM (I)}
+   \small
+   \begin{itemize}
+      \item<1->{First, a prerun has to be carried out. The domain size of the prerun has to be large enough to capture all relevant scales of turbulence.}
+      \item<2->{Restart data has to be output and output of instantaneous, horizontally averaged profiles has to be switched on and performed at the end of the run. 
+                This enables writing of profiles to the restart file, which can then be used by the main run.}
+   \end{itemize}
+   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
+   \onslide<2->{
+   \begin{tikzpicture}      
+      \node[box](inipar){ \begin{tabbing} 
+         \&d3par \= end\_time = 3600.0, \\
+                 \> dt\_dopr = 3600.0, data\_output\_pr = 'u', \\
+                 \> ....... / \\ \end{tabbing}};
+   \end{tikzpicture}}
+   \normalsize
+\end{frame}
+
+% Folie 14
+\begin{frame}
+   \frametitle{How to set up turbulence recycling with PALM (II)}
+   \small
+   \begin{itemize}
+      \item{The main run has to read the data from the precursor run (however, it is not a restart run!). This requires an extra activating string (e.g. turrec) in 
+            the file connection statement for restart data.}           
+   \end{itemize}
+   \begin{center}
+   \includegraphics[width=0.8\textwidth]{non_cyclic_figures/list_of_input_files.png}
+   \end{center} 
+   \begin{itemize}
+      \item<2->{The mrun-command to start the main run then has to look like \par\bigskip
+          {\tt mrun ... -r \dq d3\# turrec\dq}   \par\bigskip
+          The main run is allowed to use a different number of processors and a different domain decomposition than the precursor run!}
+   \end{itemize}
+\end{frame}
+
+\begin{frame}
+   \frametitle{How to set up turbulence recycling with PALM (III)}
+   \begin{itemize}
+      \item{\textbf{required} / recommended parameter settings for the main run:}
+   \end{itemize}
+   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\footnotesize]
+   \tikzstyle{box2} = [rectangle, draw, text width=0.4\textwidth, font=\tiny]
+   \tikzstyle{line} = [draw, -latex']
+   \begin{tikzpicture}      
+      \node[box](inipar){ \begin{tabbing} 
+         \&inipar \= ....... \\
+                  \\
+                  \> \textbf{turbulent\_inflow = .TRUE.}, \\ 
+                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, \\
+                  \> \textbf{psolver = 'multigrid'}, \\
+                  \> \textbf{initializing\_actions = 'cyclic\_fill'}, \\
+                  \> \textbf{recycling\_width = ...}, \\
+                  \> inflow\_damping\_height = ..., \\
+                  \> conserve\_volume\_flow = .T., \\
+                  \\
+                  \> ...... / \\ \end{tabbing}};
+      \uncover<2->{\node[box2] (horizontal_width) at (3,-0.6) {\textbf{Horizontal width of the recycling domain.}};}
+      \uncover<3->{\node[box2] (vertical_extend)  at (3,-2) {\textbf{Vertical extent of the recycling domain. If the precursor run simulated a convective boundary layer, 
+                                                information is automatically taken from the precursor data.}};}
+
+      \path<2->[line] (horizontal_width.west) -- (-1.2,-0.4);
+      \path<3->[line] (vertical_extend.west)  -- (-0.4,-0.9);
+   \end{tikzpicture}
+\end{frame}
+
+% Folie 16
+\begin{frame}
+   \frametitle{Final remarks}
+   \begin{itemize}
+      \item<1->{Non-cyclic boundary conditions and turbulence recycling method require extreme care with setting of the respective parameters.}
+      \item<2->{So far, these methods have been applied only to a few special cases (cold air outbreaks). Other setups may require modifications.}
+      \item<3->{Biggest problems are caused by gravity waves in capping inversions. Simulations with pure neutral stratification are expected to cause less problems.}
+   \end{itemize}
+\end{frame}
+
+\end{document}
Index: palm/trunk/TUTORIAL/SOURCE/numerics_bc.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/numerics_bc.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/numerics_bc.tex	(revision 915)
@@ -0,0 +1,741 @@
+% $Id$
+\input{header_tmp.tex}
+%\input{header_lectures.tex}
+
+\usepackage[utf8]{inputenc}
+\usepackage{ngerman}
+\usepackage{pgf}
+\usetheme{Dresden}
+\usepackage{subfigure}
+\usepackage{units}
+\usepackage{multimedia}
+\usepackage{hyperref}
+\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
+\usepackage{xmpmulti}
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows,positioning}
+\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{multicol}
+\usepackage{pdfcomment}
+
+\institute{Institut fÃŒr Meteorologie und Klimatologie, Leibniz UniversitÃ€t Hannover}
+\date{last update: \today}
+\event{PALM Seminar}
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamertemplate{footline}
+  {
+    \begin{beamercolorbox}[rightskip=-0.1cm]&
+     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,
+      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}
+      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}
+    \end{beamercolorbox}
+  }
+%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}}
+
+\title[Numerics and Boundary Conditions]{Numerics and Boundary Conditions\\
+(used in PALM)
+}
+\author{Siegfried Raasch}
+
+\begin{document}
+
+% Folie 1
+\begin{frame}
+\titlepage
+\end{frame}
+
+% Folie 2
+\begin{frame}
+   \frametitle{Overview}
+   \scriptsize PALM is (almost) using simple, standard and fast numerical schemes:
+   \begin{itemize}
+      \scriptsize
+      \item<2-> \textbf{Spatial and temporal discretization by finite differences}\\
+      \item<3-> \textbf{Explicit timestep methods:}\\
+         - Euler\\
+         - Leapfrog\\
+         - \underline{Runge-Kutta}, second or \underline{third order}
+      \item<4-> \textbf{Advection method}\\
+         - Upstream\\
+         - Piacsek-Williams (second order central finite differences)\\
+         - Upstream-spline\\
+         - Bott-Chlond-scheme (monotone, positiv definit, for scalars only)\\
+         - \underline{5th-order scheme of Wicker and Skamarock}, (as used in WRF model)
+      \item<5-> \textbf{Poisson-equation for pressure}\\
+         - \underline{Direct FFT-method}\\
+         - Multigrid-method
+      \item<6-> \textbf{Lagrangian particle model included}
+      \item<7-> \textbf{Boundary conditions:}\\
+         - \underline{Cyclic} and non-cyclic horizontal boundary conditions\\
+         - Surface layer with Monin-Obukhov similarity\\
+         - Topography\\
+         - Turbulent inflow (for non-cyclic horizontal boundary conditions)
+         
+   \end{itemize}
+\end{frame}
+
+
+\section{Numerics}
+\subsection{Numerics}
+
+% Folie 3
+\begin{frame}
+   \frametitle{Numerical Grid}
+   \footnotesize
+   \vspace{2mm}
+   \includegraphics[width=\textwidth]{numerics_bc_figures/numerical_grid.png}
+   \begin{itemize}
+      \item<1->Equations are spatially discretized on an Arakawa-C grid.
+      \item<2->All scalar variables s (e.g. , $p^*$, $e$, $K_{\mathrm{m}}$, 
+               $K_{\mathrm{h}}$) are defined at the cell centers.
+      \item<3->Velocity components ($u$, $v$, $w$) are shifted by half of the grid spacing.
+      \item<4->Spacings are equidistant, stretching along $z$ is possible.
+   \end{itemize}
+
+   \tikzstyle{plain} = [rectangle, draw, fill=white!20, text width=0.33\textwidth, font=\small]
+   \begin{tikzpicture}[remember picture, overlay]
+      \node at (current page.north west){%
+      \begin{tikzpicture}[overlay]
+         \node[plain, draw,anchor=west] at (88mm,-55mm) {
+         \noindent \scriptsize general definition (cylic):\\
+         $\Psi$(0:nz+1,-1:ny+1,-1:nx+1)\\
+         $\Psi$(:,-1,:) $=\Psi$(:,ny,:)\\
+         $\Psi$(:,ny+1,:) $=\Psi$(:,0,:)
+
+         };
+      \end{tikzpicture}
+      };
+   \end{tikzpicture}
+\end{frame}
+
+% Folie 4
+\begin{frame}
+   \frametitle{Timestep Methods (I)}
+   \footnotesize
+   \begin{itemize}
+      \item<1->\textbf{Euler}\\
+      \vspace{1mm}
+      $\dfrac{\partial \psi(t)}{\partial t} = F (\psi(t)) \rightarrow 
+      \dfrac{\psi(t + \Delta t) - \psi(t)}{\Delta t} 
+      \approx F (\psi(t))$ \hspace{8mm} 
+      \onslide<2-> $u\dfrac{\Delta t}{\Delta x}=C<1$\\
+      \begin{flushright}
+         for stability
+      \end{flushright}
+
+      \onslide<1->$\psi (t+\Delta t) = \psi(t) 
+      + \Delta t \cdot F(\psi(t)) \hspace{28mm} \mathcal{O}(\Delta t)$\\
+      (used for SGS-TKE in special cases)
+         
+      \vspace{3mm}
+      \item<3-> \textbf{Leapfrog}\\
+      $\psi(t + \Delta t) = \psi(t - \Delta t)+2 \Delta t \cdot F(\psi(t))$ \hspace{16mm} $
+      \mathcal{O}(\Delta t^2)$ \hspace{3mm} $C \le 0.1$\\
+      Time-splitting requires a weak time filter (Asselin filter)
+         
+      \vspace{3mm}
+      \item<4-> \textbf{Runge-Kutta, third-order}\\
+      $k_1=F(\psi(t))$\\
+      \vspace{1mm}
+      $k_2=F \left( \psi(t) + \frac{1}{3} \Delta t \cdot k_1 \right)$\\
+      \vspace{1mm}
+      $k_3=F \left( \psi(t) - \frac{3}{16} \Delta t \cdot k_1 
+      + \frac{15}{16} \Delta t \cdot k_2 \right)$\\
+      \vspace{1mm}
+      $\psi(t + \Delta t) = \psi(t) + \frac{1}{30}\Delta t (5 k_1 + 9 k_2 + 16 k_3)$ 
+      \hspace{12mm} $\mathcal{O}(\Delta t^2)$ \hspace{3mm} $C \le 0.9$\\
+   \end{itemize}
+\end{frame}
+
+% Folie 5
+\begin{frame}
+   \frametitle{Timestep Methods (II)}
+   \footnotesize
+   \onslide<1->In the PALM code, the different timestep schemes are treated by one 
+   equation using switches:
+   $\psi (t + \Delta t ) = (1 - c_1) \cdot \psi (t - \Delta t ) + c_1 \cdot \psi (t) 
+   + \Delta t \cdot \left[ c_2 \cdot F (\psi (t) ) + c_3 \cdot F (\psi (t -  
+   \Delta t ) ) \right]$
+   \vspace{1mm}
+
+   \onslide<2->
+   \begin{centering}
+      \begin{table}
+         \begin{tabular}{cccc}
+            \bf{Scheme} & \bf{c$_1$} & \bf{c$_2$} & \bf{c$_3$}\\
+            Euler & 1 & 1 & 0\\
+            Leapfrog & 0 & 2 & 0\\
+            RK (1st step) & 1 & 1/3 & 0\\
+            RK (2nd step) & 1 & 15/16 & -25/48\\
+            RK (3rd step) & 1 & 8/15 & 1/15\\
+         \end{tabular}
+      \end{table}
+   \end{centering}
+
+   \onslide<3->
+   \begin{align*}
+      \psi (t - \Delta t) &= \psi (t) \hspace{15mm} \textbf{after each RK substep}\\
+      \psi (t) &= \psi (t + \Delta t)
+   \end{align*}
+\end{frame}
+
+% Folie 6
+\begin{frame}
+   \frametitle{Advection Methods (I)}
+   \small
+   \begin{itemize}
+      \item<1-> Piacsek Williams C3 (1970, J. Comput. Phy., 6, 392).
+      \item<2-> Scheme of 2nd order accuracy.
+      \item<3-> Conserves integrals of linear and quadratic quantities.
+      \item<4-> Requires incompressibility $\rightarrow$ flux form of advection term.
+                \onslide<4-> \includegraphics[width=0.8\textwidth]{numerics_bc_figures/advection_methods.png}
+   \end{itemize}
+   $$\left.\frac{\partial (u \psi)}{\partial x}\right\vert_i = \frac{1}{2 \Delta x} 
+   \left( u_{i+\frac{1}{2}} \psi_{i+1} - u_{i-\frac{1}{2}} \psi_{i-1} \right)$$
+   \begin{itemize}
+      \item<5-> In case of momentum advection (e.g. $\psi=u$), $u_{i-1}$ and 
+                $u_{i+1}$ have to be obtained by linear interpolation.
+      \item<5-> May cause $2 \Delta x$ wiggles in case of sharp gradients.
+   \end{itemize}
+\end{frame}
+
+% Folie 7
+\begin{frame}
+   \frametitle{Advection Methods (II)}
+   \begin{itemize}
+      \item<1-> \small Upstream-spline\\ \scriptsize
+         \onslide<1-> - Requires Euler timestep\\
+         \onslide<2-> - Nonlocal scheme: produces heavy load on communication network\\
+         \onslide<3-> - Numerically unstable under stable stratification
+      \item<4-> \small Bott-Chlond\\ \scriptsize
+         \onslide<4-> - Chlond (1994)\\
+         \onslide<5-> - Monotone, positive definit. Can only be used for scalars\\
+         \onslide<6-> - Conserves sharp gradients\\
+         \onslide<7-> - Numerically expensive\\
+         \onslide<8-> - Not optimized for use on cache-based machines.
+      \item<9-> \small Default: Wicker and Skamarock scheme (5th order)\\ \scriptsize
+         \onslide<9-> - Much better accuracy than Piacsek Williams\\
+         \onslide<10-> - Much simpler algorithm than Bott-Chlond\\
+         \onslide<11-> - Requires additional ghost layers\\
+         \onslide<12-> - Adds additional numerical dissipation
+         
+   \end{itemize}
+\end{frame}
+
+% Folie 8
+\begin{frame}
+   \frametitle{Advection Methods â Wicker/Skamarock (I)}
+   \footnotesize
+   \begin{itemize}
+      \item Wicker and Skamarock (2002, Mon. Wea. Rev. 130, 2088 â 2097).
+      \item Based on flux form of advection term
+      \item Difference of fluxes at the edge of the grid cell is used to 
+      discretise advection term
+   \end{itemize}
+
+   \begin{columns}[T]
+      \begin{column}{0.55\textwidth}
+         \hspace{8mm}\includegraphics[width=0.8\textwidth]{numerics_bc_figures/numerical_grid_small.png}
+      \end{column}
+      \begin{column}{0.45\textwidth}
+         $\frac{ \partial \psi}{\partial t} = - \nabla (u_i \psi) \approx 
+         - \frac{F_{i+\frac{1}{2}} - F_{i-\frac{1}{2}}}{\Delta x}$
+      \end{column}
+   \end{columns}
+
+   \tikzstyle{plain} = [rectangle, text width=0.1\textwidth, font=\small]
+   \begin{tikzpicture}[remember picture, overlay]
+      \node at (current page.north west){%
+
+      \begin{tikzpicture}[overlay]
+         \node[plain, anchor=west] at (2mm,-68mm) {
+         \tikz 
+         {
+         \draw[blue, -latex', line width=5pt] (1,0) -- (2,0);
+         }
+
+         $F_{i-\frac{1}{2}}$
+         };
+      \end{tikzpicture}
+
+      \begin{tikzpicture}[overlay]
+         \node[plain, anchor=west] at (62mm,-68mm) {
+         \tikz 
+         {
+         \draw[blue, -latex', line width=5pt] (,0) -- (2,0);
+         }
+         $F_{i+\frac{1}{2}}$
+         };
+      \end{tikzpicture}
+
+      };
+   \end{tikzpicture}
+\end{frame}
+
+% Folie 9
+\begin{frame}
+   \frametitle{Advection Methods â Wicker/Skamarock (II)}
+   
+
+
+   \textbf{Finite difference approxiamtion of 6$^{\text{th}}$ order}
+   \begin{tikzpicture}[scale=2]
+      \tikzstyle{ann} = [draw=none,fill=none,right]
+      \matrix[nodes={draw, thick, fill=blue!20}, row sep=0.3cm,column sep=0.5cm]{
+      \node[rectangle, rounded corners]{
+      $F^{\text{6th}}_{i-\frac{1}{2}} = \frac{1}{60} u_{i-\frac{1}{2}} \left( 37 
+      (\Psi_i + \Psi_{i-1}) - 8 (\Psi_{i+1} + \Psi_{i-2}) + (\Psi_{i+2} 
+      + \Psi_{i-3}) \right)$ 
+       };\\
+       };
+   \end{tikzpicture}
+   
+   \vspace{5mm}
+   
+   \textbf{Artificially added numerical dissipation term}
+   \begin{tikzpicture}[scale=2]
+      \tikzstyle{ann} = [draw=none,fill=none,right]
+      \matrix[nodes={draw, thick, fill=blue!40}, row sep=0.3cm,column sep=0.5cm]{
+      \node[rectangle, rounded corners]{
+      $\frac{-1}{60} \left| u_{i-\frac{1}{2}} \right| \left( 10 (\Psi_i - 
+      \Psi_{i-1}) - 5 (\Psi_{i+1} - \Psi_{i-2}) + (\Psi_{i+2} - \Psi_{i-3}) \right)$ 
+       };\\
+       };
+   \end{tikzpicture}
+\end{frame}
+
+% Folie 10
+\begin{frame}
+   \frametitle{Advection Methods â Wicker/Skamarock (III)}
+   
+   \begin{tikzpicture}[scale=2]
+      \tikzstyle{ann} = [draw=none,fill=none,right]
+      \matrix[nodes={draw, thick, fill=blue!20}, row sep=0.3cm,column sep=0.5cm]{
+      \node[rectangle, rounded corners]{
+      $F^{\text{6th}}_{i-\frac{1}{2}} = \frac{1}{60} u_{i-\frac{1}{2}} 
+      \left( 37 (\Psi_i + \Psi_{i-1}) - 8 (\Psi_{i+1} + \Psi_{i-2}) + (\Psi_{i+2} + 
+      \Psi_{i-3}) \right)$ 
+       };\\
+       };
+   \end{tikzpicture}
+   
+   \begin{columns}[T]
+      \begin{column}{0.7\textwidth}
+         \includegraphics[width=1\textwidth]{numerics_bc_figures/numerical_oscillations.png}
+      \end{column}
+      \begin{column}{0.3\textwidth}
+         Centered Finite Differences produces numerical oscillations (''wiggles'') 
+         near sharp gradients.
+      \end{column}
+   \end{columns}
+\end{frame}
+
+% Folie 11
+\begin{frame}
+   \frametitle{Advection Methods â Wicker/Skamarock (IV)}
+   \footnotesize
+   
+   \begin{columns}[T]
+      \begin{column}{0.1\textwidth}
+            \begin{tikzpicture}[scale=2]
+      \tikzstyle{ann} = [draw=none,fill=none,right]
+      \matrix[nodes={draw, thick, fill=blue!40}, row sep=0.3cm,column sep=0.5cm]{
+      \node[draw=none,fill=none]{
+      $F^{\text{5th}}_{i-\frac{1}{2}} = F^{\text{6th}}_{i-\frac{1}{2}}$
+      };\\
+       };
+   \end{tikzpicture}
+      \end{column}
+      \begin{column}{0.8\textwidth}
+            \begin{tikzpicture}[scale=2]
+      \tikzstyle{ann} = [draw=none,fill=none,right]
+      \matrix[nodes={draw, thick, fill=blue!40}, row sep=0.3cm,column sep=0.5cm]{
+      \node[rectangle, rounded corners]{
+      $- \frac{1}{60} \left| u_{i-\frac{1}{2}} \right| \left( 10 (\Psi_i - \Psi_{i-1}) - 
+      5 (\Psi_{i+1} - \Psi_{i-2}) + (\Psi_{i+2} - \Psi_{i-3}) \right)$ 
+       };\\
+       };
+   \end{tikzpicture}
+      \end{column}
+   \end{columns}
+   
+   \begin{columns}[T]
+      \begin{column}{0.7\textwidth}
+         \includegraphics[width=1\textwidth]{numerics_bc_figures/numerical_oscillations_2.png}
+      \end{column}
+      \begin{column}{0.3\textwidth}
+         \vspace{3mm}
+         \underline{Advantage}\\
+         Numerical Dissipation damps small scale oscillations.\\
+         \vspace{3mm}
+         \underline{Disadvantage}\\
+         In a turbulent flow numerical dissipation removes energy from small scales.
+
+      \end{column}
+   \end{columns}
+\end{frame}
+
+% Folie 12
+\begin{frame}
+   \frametitle{Advection Methods â Wicker/Skamarock (V)}
+    
+    \begin{columns}[T]
+      \begin{column}{0.6\textwidth}
+         \includegraphics[width=1\textwidth]{numerics_bc_figures/numerical_properties.png}
+      \end{column}
+      \begin{column}{0.4\textwidth}
+         \includegraphics[width=1\textwidth]{numerics_bc_figures/pw_ws.png}
+      \end{column}
+   \end{columns}
+    
+   \begin{itemize}
+      \item Better resolution of larger scales $(> 8\,\Delta x)$ and hence less 
+      numerical energy transfer from larger to smaller scales compared to lower 
+      order schemes.
+      \item Less spectral energy at smaller scales.
+   \end{itemize}
+   
+\end{frame}
+
+% Folie 13
+\begin{frame}
+   \frametitle{Pressure Solver (I)}
+   \footnotesize
+   \begin{itemize}
+      \item<1-> Governing equations of PALM require incompressibility
+      \item<2-> Incompressibility is reached by a predictor-corrector method\\
+            \scriptsize
+            1. Momentum equations are solved without the pressure term giving a
+            provisional velocity field which is not free of divergence.\\
+            $\overline{u}^{t+\Delta t}_{i_{\mathrm{prov}}} = \overline{u}^t_i +
+            \Delta t \left( - \frac{\partial}{\partial x_k} \overline{u}^t_k
+            \overline{u}^t_i - (\varepsilon_{ijk} f_j \overline{u}^t_k 
+            - \varepsilon_{i3k} f_3 u_{\mathrm{g}_k}) 
+            + g \frac{\overline{\theta^*}^t}{\theta_0} \delta_{i3} 
+            - \frac{\partial}{\partial x_k} \overline{u'_k u'_i}^t \right)$\\
+            \vspace{3mm}
+            \onslide<3-> 2. Assign all remaining divergences to the (perturbation)
+            pressure $p^*$ so that the new corrected velocity field is the sum of the
+            provisional, divergent field and the perturbation pressure term.\\
+            $\overline{u}^{t+\Delta t}_{i} = 
+            \overline{u}^{t+\Delta t}_{i_{\mathrm{prov}}} - 
+            \frac{\Delta t}{\rho_0} \frac{\partial \overline{p^*}^t}{\partial x_i}$\\
+            \vspace{3mm}
+            \onslide<4-> 3. The divergence operator is applied to this equation.
+            Demanding a corrected velocity field free of divergence, this leads to a
+            Poisson equation for the perturbation pressure.\\
+            $\frac{\partial^2 \overline{p^*}^t}{\partial x_i^2} = \frac{\rho_0}
+            {\Delta t} \frac{\partial \overline{u}_{i_{\mathrm{prov}}}^{t + \Delta t}}
+            {\partial x_i}$\\
+            \vspace{3mm}
+            \onslide<5-> 4. After solving the Poisson equation, the final velocity field
+            is \\
+            calculated as given in step 2.\\
+
+   \end{itemize}
+\end{frame}
+
+% Folie 14
+\begin{frame}
+   \frametitle{Pressure Solver (II)}
+   \small
+   
+   \begin{itemize}
+      \item FFT-solver\\
+      \onslide<1-> 1. Discretization of the Poisson-equation by central differences\\
+      \onslide<2-> 2. 2D discrete FFT in both horizontal directions\\
+      \onslide<3-> 3. Solving the resulting tridiagonal set of linear equations\\
+      \onslide<4-> 4. Inverse 2D discrete FFT in both horizontal directions leading 
+      to the perturbation pressure
+
+      \begin{itemize}
+         \item<5-> Very fast and accurate, $\mathcal{O}(n \log n)$, $n$: 
+         number of gridpoints
+         \item<6-> CPU requirement $<$ 50\% of total CPU time
+         \item<7-> Due to non-locality of the FFT, transpositions are required 
+         on parallel computers
+         \item<8-> Usage requires periodic boundary conditions and uniform grids 
+         along $x$ and $y$
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 15
+\begin{frame}
+   \frametitle{Pressure Solver (III)}
+   \scriptsize   
+   \begin{columns}
+      \begin{column}{1.03\textwidth}
+         \begin{itemize}
+            \item<1-> Multigrid-method\\
+            \begin{itemize}\scriptsize  
+               \item Iterative solver\\
+               \scriptsize
+               basic idea: Poisson equation is transformed to a fixed point problem:\\
+               $\vec{p}^{k+1} = T \cdot \vec{p}^k + \vec{c}^k$\\
+               \vspace{1mm}
+               \onslide<2-> starting from a first guess, the solution will be 
+               improved by repeated execution of the fixed point problem:\\
+               $\begin{array}{rcl}
+               \vec{p}^{1} &=&T \cdot \vec{p}^0 + \vec{c}^0\\
+               \vec{p}^{2} &=&T \cdot \vec{p}^1 + \vec{c}^1
+               \vspace{-2mm}\\
+               
+               &\vdots&
+               \vspace{-1.5mm}\\
+               
+               \vec{p}^{k} &=&T \cdot \vec{p}^{k-1} + \vec{c}^{k-1}\\
+               \vec{p}^{k+1} &=&T \cdot \vec{p}^k + \vec{c}^k\\
+               \end{array}$\\
+               \vspace{1mm}
+               \onslide<3-> Depending on the structure of the matrix $T$ and vector 
+               $c$ different iterative solvers can be defined, e.g.: Jacobi-scheme 
+               (here on 2D-uniform grid):\\
+               $p^{k+1}_{i,j} = \frac{1}{4} \cdot \left( p^k_{i-1,j} + p^k_{i+1,j} 
+               + p^k_{i,j-1} + p^k_{i,j+1} - \Delta x^2 f(i,j,k) \right)$\\
+               \scriptsize \vspace{2mm}
+               \item<4-> With each iteration step $k$ the improved solution converges towards 
+               the exact solution.
+               \item<5-> Iterative schemes are 'local schemes' $\rightarrow$ information 
+               is needed \\ only from neighboring grid-points.
+               \item<6-> Very low convergence: $\mathcal{O}(n^2)$.
+           \end{itemize}
+         \end{itemize}
+      \end{column}
+   \end{columns}
+\end{frame}
+   
+% Folie 16
+\begin{frame}
+   \frametitle{Pressure Solver (IV)} 
+   \begin{itemize}
+      \item<1-> Multigrid-method\\
+      \begin{itemize}
+         \item Due to their locality, iterative solvers show a frequency-dependent
+            reduction of the residual: low frequencies are reduced slower than high
+            frequencies.
+         \item<2-> The main idea of the multigrid method is to reduce errors of different
+         frequencies on grids with different grid spacing:
+         \begin{itemize}
+            \item errors of high frequency are reduced on fine grids
+            \item errors of low frequency are reduced on coarse grids.
+         \end{itemize}
+      \end{itemize}
+   \end{itemize}
+   \onslide<2->
+   \begin{figure}[htp]
+      \centering
+      \includegraphics[scale=0.35]{numerics_bc_figures/errors.png}
+   \end{figure}
+\end{frame}
+
+% Folie 17
+\begin{frame}
+   \frametitle{Pressure Solver (V)} 
+   
+   \begin{columns}[T]
+      \begin{column}{0.65\textwidth}
+         \begin{itemize}
+            \item<1-> Multigrid-method\\
+            \begin{itemize}
+               \footnotesize
+               \item On each grid-level an approximate solution of the fixed point 
+                  equation is obtained performing a few iterations.
+               \item<2-> The solution is transmitted to the next coarser grid-level
+                  where it is used as the first guess to solve the fixed point problem.
+               \item<3-> This procedure is performed up to the coarsest grid-level
+                  containing two grid-points in each direction.
+               \item<4-> From the coarsest grid-level the procedure is passed in 
+                  backward order to get the final solution.
+               \item<5-> For large grids faster than FFT method.
+               \item<6-> V- and W-cycles are implemented.
+            \end{itemize}
+      \end{itemize}
+      \end{column}
+      \begin{column}{0.5\textwidth}
+         \onslide<2->
+         \includegraphics[width=1\textwidth]{numerics_bc_figures/multigrid.png}
+      \end{column}
+   \end{columns}
+\end{frame}
+
+
+
+\section{Boundary Conditions}
+\subsection{Boundary Conditions}
+
+% Folie 18
+\begin{frame}
+   \frametitle{Boundary Conditions (I)}
+   
+   \begin{itemize}
+      \item<1-> Lateral $(xy)$ boundary conditions:\\
+      \begin{itemize}
+         \item Cyclic by default, allowing undisturbed evolution / advection of turbulence.
+            \begin{columns}[T]
+               \begin{column}{0.2\textwidth}
+                  %leer
+               \end{column}
+               \begin{column}{0.5\textwidth}
+                  \includegraphics[width=1\textwidth]{numerics_bc_figures/lateral_bc.png}\\
+                  \vspace{2mm}
+               \end{column}
+               \begin{column}{0.4\textwidth}
+                  $\begin{array}{rcl}
+                     \Psi(-1) &=& \Psi(n)\\
+                     \Psi(n+1) &=& \Psi(0)\\
+                  \end{array}$
+               \end{column}
+            \end{columns}
+   
+         \item<2-> Dirichlet (inflow) and radiation (outflow) conditions are allowed along
+            either $x$- or $y$-direction.
+
+         \item<3-> In case of a Dirichlet condition, the inflow is laminar (by default) and 
+            the domain has to be extended to allow for the development of a turbulent
+            state, if neccessary.
+         \item<4->  Non-cyclic lateral conditions require the use of the multigrid-method 
+            for solving the Poisson-equation.
+            
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 19
+\begin{frame}
+   \frametitle{Boundary Conditions (II)}
+   
+   \begin{columns}[T]
+      \begin{column}{0.7\textwidth}
+         \scriptsize
+         \begin{itemize}
+            \item<1-> Surface boundary condition:
+            \begin{itemize}
+               \scriptsize
+               \item<1-> Monin-Obukhov-similarity is used by default, i.e. a Prandtl-layer is 
+                  assumed between the surface and the first grid layer.\\
+                  $\frac{\partial \overline{u}}{\partial z} = \frac{u_{*}}{\kappa z} 
+                  \Phi_{\mathrm{m}}$; \hspace{3mm} $u_{*} = \sqrt{- \overline{w' u'_0}} 
+                  = \sqrt{\frac{\tau_0}{\overline{\rho}}}$\\
+                  $\frac{\partial \overline{\theta}}{\partial z} = \frac{\vartheta_{*}}
+                  {\kappa z} \Phi_{\mathrm{h}}$; \hspace{3mm} $\vartheta_{*} = 
+                  \frac{\overline{w' \theta'_0}}{u_{*}}$\\
+               \vspace{2mm}
+               \item<2-> Integration between $z=z_0$ (roughness height) and $z=z_{\mathrm{p}}$
+                  (top of Prandtl-layer, $k=1$) gives the only unknowns $u_{*}$ and
+                  $\theta_{*}$ which then define the surface momentum and heat flux,
+                  used as the real boundary conditions.\\
+               \vspace{2mm}
+               \item<3-> $\Phi_{\mathrm{m}}$, $\Phi_{\mathrm{h}}$: Dyer-Businger functions\\
+               \onslide<4->$\Phi_{\mathrm{m}} = \left\{ \begin{array}{cc}
+                     1+5\,\mathrm{Rif} & \text{stable}\\
+                     1 & \text{neutral}\\
+                     (1-16\,\mathrm{Rif})^{-1/4} & \text{unstable}\\
+                  \end{array} \right. $
+
+            \end{itemize}
+         \end{itemize}
+      \end{column}
+      \begin{column}{0.3\textwidth}
+         \onslide<1->
+         \includegraphics[width=1\textwidth]{numerics_bc_figures/surface_bc.png}\\
+         \vspace{-2mm}
+         Prandtl-layer\\
+         \vspace{8mm}
+         \onslide<5->
+         $\mathrm{Rif} = \frac{\frac{g}{\tilde{\theta}} 
+         \overline{w' \theta'_0}}{\overline{w' u'} 
+         \frac{\partial \overline{u}}{\partial z}}$\\
+         \scriptsize Richardson flux number
+      \end{column}
+   \end{columns}
+\end{frame}
+
+% Folie 20
+\begin{frame}
+   \frametitle{Boundary Conditions (III)}
+
+   \begin{itemize}
+      \item<1-> Surface boundary condition:
+      \begin{itemize}
+         \footnotesize
+         \item<1-> Monin-Obukhov-similarity is only valid for a 
+            horizontal surface with homogeneous conditions.
+         \item<2-> The surface temperature has to be prescribed.
+            Alternatively, the surface heat flux can be prescribed.
+         \item<3-> Instead of MO-similarity, no-slip conditions or
+            free-slip conditions can be used
+            \begin{equation*}
+               u(z=0) = 0, \quad v(z=0)=0 \hspace{15mm}
+               \frac{\partial u}{\partial z} = 0, \quad 
+               \frac{\partial v}{\partial z} = 0 \qquad
+            \end{equation*}
+            realized by 
+            \begin{flalign*}
+               u(k=0)=-u(k=1) \hspace{18mm} u(k=0)=u(k=1)\\
+               v(k=0)=-v(k=1) \hspace{18mm} v(k=0)=v(k=1)
+            \end{flalign*}
+         \item<4-> Pressure boundary condition: 
+            $\dfrac{\partial p}{\partial z} = 0$ 
+            in order to guarantee $w(z=0)=0$
+         \item<5-> SGS-TKE condition $\dfrac{\partial e}{\partial z}=0$
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 21
+\begin{frame}
+   \frametitle{Boundary Conditions (IV)}
+
+   \begin{itemize}
+      \item<1-> Boundary conditions at the top (default)
+      \begin{itemize}
+         \item<1-> Dirichlet conditions for velocities: $u=u_{\mathrm{g}}, 
+            \quad v=v_{\mathrm{g}}, \quad w=0$
+         \item<2-> Neumann conditions (temporal constant gradients) for scalars:
+            $$\frac{\partial \theta}{\partial z} = 
+            \left. \frac{\partial \theta}{\partial z} \right\vert_{t=0}$$
+         \item<3-> Pressure: Dirichlet $p=0$ 
+            or Neumann $\dfrac{\partial p}{\partial z} = 0$
+         \item<4-> SGS-TKE: Neumann $\dfrac{\partial e}{\partial z} = 0$
+         \item<5-> A damping layer can be switched on in order to absorb 
+            gravity waves.
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 22
+\begin{frame}
+   \frametitle{Initial Conditions}
+
+   All 3D-arrays are initialized with vertical profiles (horizontally homogeneous).\\
+   \quad \\
+   Two different profiles can be chosen:
+   \begin{itemize}
+      \item<2-> \textbf{constant (piecewise linear) profiles}
+         \begin{itemize}
+            \footnotesize
+            \item \textbf{e.g.} $u=0, v=0, \dfrac{\partial \theta}{\partial z}=0$ 
+               \textbf{up to} $z=\unit[1000]{m}$, 
+               $\dfrac{\partial \theta}{\partial z}=+1.0$ \textbf{up to top}
+         \end{itemize}
+      \item<3-> \textbf{velocity profiles calculated by a 1D-model (which is a part of PALM)}
+         \begin{itemize}
+            \footnotesize
+            \item  \textbf{constant (piecewise linear) temperature profile is used 
+               for the 1D-model}
+         \end{itemize}
+   \end{itemize}
+   \onslide<4->
+   \underline{Under horizontally homogeneous initial conditions, random}\\ 
+   \underline{fluctuations have to be added in order to generate turbulence!}
+\end{frame}
+
+\end{document}
Index: palm/trunk/TUTORIAL/SOURCE/palm_overview.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/palm_overview.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/palm_overview.tex	(revision 915)
@@ -0,0 +1,439 @@
+% $Id$
+\input{header_tmp.tex}
+%\input{header_lectures.tex}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{pgf}
+\usetheme{Dresden}
+\usepackage{subfigure}
+\usepackage{units}
+\usepackage{multimedia}
+\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
+\usepackage{xmpmulti}
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows,positioning}
+\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+
+\institute{Institut fÃŒr Meteorologie und Klimatologie, Leibniz UniversitÃ€t Hannover}
+\date{last update: \today}
+\event{PALM Seminar}
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamertemplate{footline}
+  {%
+    \begin{beamercolorbox}[rightskip=-0.1cm]&
+     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
+      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
+      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
+    \end{beamercolorbox}%
+%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
+%    \end{beamercolorbox}
+  }
+%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.png}}
+
+\title[PALM Overview]{PALM Overview}
+\author{Siegfried Raasch}
+
+
+% Notes:
+% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
+% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
+\begin{document}
+
+\begin{frame}
+\titlepage
+\end{frame}
+
+\section{PALM Overview}
+\subsection{PALM Overview}
+
+%Folie 01
+\begin{frame}
+   \begin{center}
+      PALM - Overview
+   \end{center}
+\end{frame}
+
+%Folie 02
+\begin{frame}
+   \frametitle{PALM - Overview}
+   \begin{flushleft}
+      \textbf{PA}rallelized \textbf{L}ES \textbf{M}odel
+   \end{flushleft}
+   \begin{itemize}
+      \item<2->{First version 1997, continously developed since then}
+      \item<3->{Written in FORTRAN 95}
+      \item<4->{Very high performance and scalability on all state-of-the-art parallel architectures}
+      \item<5->{One code for atmosphere and ocean}
+      \item<6->{Code is free to use for scientific applications}
+   \end{itemize}
+\end{frame}
+
+%Folie 03
+\begin{frame}
+   \frametitle{PALM - Overview}
+   \begin{flushleft}
+      \textbf{Software-development in a professional environment}
+   \end{flushleft}
+   \begin{itemize}
+      \item<2->{Detailed online-documentation}
+      \item<3->{Interface for code-extensions by users}
+      \item<4->{Code is managed and distributed via subversion }
+      \begin{itemize}
+         \item<5->{Direct code-access from the internet}
+         \item<6->{Allows collaborative code-development}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+%Folie 04
+\begin{frame}
+   \frametitle{PALM - Features (General Overview)}
+   \framesubtitle{Physics / Numerics        (special characteristics)}
+   \begin{itemize}
+      \item<2->{Cyclic horizontal boundary conditions but also non-cyclic boundary conditions along x or y available}
+      \item<3->{Turbulent inflow is realized for non-cyclic boundary conditions}
+      \item<4->{Topography can be used}
+      \item<5->{A Lagrangian particle model is embedded}
+      \item<6->{Code can be switched to ocean, i.e. salinity equation and equation of state for seawater is included}
+      \item<7->{Coupled ocean-atmosphere simulations are possible}
+      \item<8->{A simple canopy model is included}
+      \item<9->{It allows for very huge applications\\ (currently $4000^{3}$ gridpoints)}
+   \end{itemize}
+\end{frame}
+
+%Folie 05
+\begin{frame}
+   \frametitle{PALM - Features (General Overview)}
+   \begin{flushleft}
+      \textbf{Technical features}
+   \end{flushleft}
+   \begin{itemize}
+      \item<2->{Scripts allow for very comfortable operation of the model}
+      \item<3->{Model can be adapted for any kind of (Unix) system by simply adjusting a configuration file}
+      \item<4->{Batch jobs and job chains (restart mechanism) can be automatically created (requires manual adjustments of scripts)}
+      \item<5->{Runs are controlled by a simple NAMELIST parameter file}
+      \item<6->{ Error messages inform in case of parameter inconsistencies or other problems detected during runtime}
+   \end{itemize}
+\end{frame}
+
+%Folie 06
+\begin{frame}
+   \frametitle{PALM - Features (General Overview)}
+   \begin{flushleft}
+      \textbf{Technical features}
+   \end{flushleft}
+   \begin{itemize}
+      \item<1->{Standard data analysis is done within the simulation itself}
+      \item<2->{All output is in standard netCDF data format}
+      \item<3->{A user-interface allows for easy code extensions by the user}
+      \item<4->{A powerful 3D-visualization software is included in the code (requires additional graphics library, (a streaming server), and a plugin for web-browsers)}
+   \end{itemize}
+\end{frame}
+
+%Folie 07
+\begin{frame}
+   \begin{figure}
+      \href{/home/maronga/dvr/data/rinne_1.html}{\includegraphics<3,5,7,9,11>[height=0.35\textheight]{palm_overview_figures/Fig08_mini_Luepkes.png}}
+      \href{Link 2}{\includegraphics<5,7,9,11>[height=0.35\textheight]{palm_overview_figures/Fig09_mini_Raasch_Franke.png}}
+      \href{Link 3}{\includegraphics<7,9,11>[height=0.35\textheight]{palm_overview_figures/Fig10_mini_gryschka.png}}
+      \href{Link 4}{\includegraphics<9,11>[height=0.35\textheight]{palm_overview_figures/Fig11_mini_steinfeld.png}}
+      \href{Link 5}{\includegraphics<11>[height=0.35\textheight]{palm_overview_figures/Fig07_mini_Letzel.png}}
+   \end{figure}
+   \begin{center}
+      \includegraphics<1>[height=0.82\textheight]{palm_overview_figures/Fig05_land.png}
+      \includegraphics<2>[height=0.82\textheight]{palm_overview_figures/Fig06_ice.png}
+      \includegraphics<4>[height=0.82\textheight]{palm_overview_figures/Fig04_staubteufel.png}
+      \includegraphics<6>[height=0.82\textheight]{palm_overview_figures/Fig03_clouds.png} 
+      \includegraphics<8>[height=0.82\textheight]{palm_overview_figures/Fig02_Mast.png}
+      \includegraphics<10>[height=0.82\textheight]{palm_overview_figures/Fig01_letzel_building.png}
+   \end{center}
+\end{frame}
+
+%Folie 08
+\begin{frame}
+   \frametitle{PALM â External Users / Areas of Application}
+   \begin{itemize}
+      \item<1->{Users / Collaborations}
+      \begin{itemize}
+         \item<2->{\textbf{AWI} Alfred Wegener Institute for Polar Research (Bremerhaven, Germany)}
+         \item<3->{\textbf{ForWind} (University of Oldenburg, Germany)}
+         \item<4->{\textbf{NERSC} Nansen Environmental And Remote Sensing Center (Bergen, Norway)}
+         \item<5->{\textbf{FMI} Finnish Meteorological Institute (Helsinki, Finland)}
+         \item<6->{Department of Atmospheric Sciences, \textbf{Yonsei University} (Seoul, Korea)}
+         \item<7->{\textbf{IGSES} (Interdisciplinary Graduate School of Engineering Sciences), \textbf{Kyushu University} (Fukuoka, Japan)}
+         \item<8->{School of Earth and Environmental Science, \textbf{Seoul National University} (Seoul, Korea)}
+         \item<9->{Dept. of Intl. Development Eng., \textbf{Tokyo Institute of Technology} (Tokyo, Japan)}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+%Folie 09
+\begin{frame}
+   \frametitle{PALM â External Users / Areas of Application}
+   \begin{itemize}
+      \item<1->{Areas of Application}
+      \begin{itemize}
+         \item<2->{Interaction of boundary layer turbulence $\leftrightarrow$ wind energy converters}
+         \item<3->{Improvement of turbulence parameterizations}
+         \item<4->{Atmosphere-ocean coupling}
+         \item<5->{Ocean mixed layer}
+         \item<6->{Turbulence in the urban canopy layer}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+\section{Technical Issues}
+\subsection{Technical Issues}
+
+%Folie 10
+\begin{frame}
+   \begin{center}
+      PALM - Overview\\
+      Technical Issues
+   \end{center}
+\end{frame}
+
+%Folie 11
+\begin{frame}
+   \tikzstyle{green} = [rectangle, draw, fill=green!20, text width=0.15\textwidth, font=\scriptsize]
+   \tikzstyle{white} = [rectangle, text width=0.4\textwidth, font=\tiny]
+   \tikzstyle{line} = [draw, -]
+   \tikzstyle{alert} = [rectangle, draw, text width=0.77\textwidth, font=\scriptsize]
+
+   \frametitle{PALM - Components - Overview}
+   The PALM download not only contains the modelâs FORTRAN code but a variety of further components / files.
+   The directory structure is as follows.\\
+   \ \\
+   \begin{tikzpicture}[auto, node distance=0]
+      \node [green] (first) {
+      \textbf{trunk} };
+      \uncover<1->{\node [white, right=1cm of first] (second) {};}
+      \uncover<2->{\node [green, above=2cm of second] (third) {\textbf{DOC/}};}
+      \uncover<3->{
+      \node [green, below=0.3cm of third] (fourth) {\textbf{EXAMPLES/}};}
+      \uncover<4->{\node [green, below=0.25cm of fourth] (fifth) {\textbf{INSTALL/}};}
+      \uncover<5->{\node [green, below=0.25cm of fifth] (sixth) {\textbf{SCRIPTS/}};}
+      \uncover<6->{\node [green, below=0.25cm of sixth] (seventh) {\textbf{SOURCE/}};}
+      \uncover<7->{\node [green, below=0.25cm of seventh] (eighth) {\textbf{UTIL/}};}
+      \uncover<2->{\node [white, right=0.25cm of third] (ninth) {\textbf{complete documentation, also accessible from the PALM homepage}};}
+      \uncover<3->{\node [white, right=0.25cm of fourth] (tenth) {\textbf{parameter files and run control output for a variety of application examples}};}
+      \uncover<4->{\node [white, right=0.25cm of fifth] (eleventh) {\textbf{parameter file and run control output to check and verify the PALM installation}};}
+      \uncover<5->{\node [white, right=0.25cm of sixth] (twelfth) {\textbf{shell scripts and helper programs for running PALM, default configuration files for the shell scripts}};}
+      \uncover<6->{\node [white, right=0.25cm of seventh] (thirteen) {\textbf{PALM source code + Makefile}};}
+      \uncover<7->{\node [white, right=0.25cm of eighth] (fourteen) {\textbf{source code for helper programs}};}
+      \uncover<8->{\node [alert, below=2cm of second] (alert) {\textcolor{red}{Please never modify or delete files in trunk and its subdirectories!}};}
+
+      \path<2-> [line] (first.east) -- (third.west);
+      \path<3-> [line] (first.east) -- (fourth.west);
+      \path<4-> [line] (first.east) -- (fifth.west);
+      \path<5-> [line] (first.east) -- (sixth.west);
+      \path<6-> [line] (first.east) -- (seventh.west);
+      \path<7-> [line] (first.east) -- (eighth.west);
+   \end{tikzpicture}
+\end{frame}
+
+%Folie 12
+\begin{frame}
+   \frametitle{Recommended Directory Structure for the PALM Installation}
+   \tikzstyle{green} = [rectangle, draw, fill=green!20, text width=0.2\textwidth, font=\Tiny]
+   \tikzstyle{yellow1} = [rectangle, draw, fill=yellow!20, text width=0.2\textwidth, font=\Tiny]
+   \tikzstyle{yellow} = [rectangle, draw, fill=yellow!20, text width=0.12\textwidth, font=\Tiny]
+   \tikzstyle{white} = [rectangle, text width=0.12\textwidth, font=\Tiny]
+   \tikzstyle{white1} = [rectangle, text width=0.2\textwidth, font=\Tiny]
+   \tikzstyle{line} = [draw, -]
+
+   \begin{tikzpicture}[auto, node distance=0]
+      \uncover<1->{\node [yellow] (first) {\textbf{\$HOME/} };}
+      \uncover<2->{\node [yellow, right=0.25cm of first] (second) {\textbf{palm/}};}
+      \uncover<3->{\node [yellow, right=0.25cm of second] (third) {\textbf{current\_version/}};}
+      \uncover<4->{\node [green, right=0.75cm of third] (fourth) {\textbf{trunk/}};}
+      \uncover<5->{\node [yellow, above=0.5cm of second] (fifth) {\textbf{job\_queue/}};}
+      \uncover<6->{\node [yellow, below=1cm of third] (sixth) {\textbf{older\_version/}};}
+      \uncover<7->{\node [yellow1, above=1.5cm of fourth] (seventh) {\textbf{JOBS/}};}
+      \uncover<8->{\node [yellow1, above=0.5cm of fourth] (eighth) {\textbf{USER\_CODE/}};}
+      \uncover<9->{\node [green, below=0.5cm of fourth] (ninth) {\textbf{MAKE\_DEPOSITORY\_.../}};}
+      \uncover<10->{\node [green, below=1.5cm of fourth] (tenth) {\textbf{MAKE\_DEPOSITORY\_.../}};}
+      \uncover<11->{\node [green, below=2.75cm of first] (eleventh) {\textbf{/tmp\_user\_catalog/}};}
+      \uncover<12->{\node [yellow1, below=3.5cm of first] (twelfth) {\textbf{/tmp\_data\_catalog/}};}
+      \uncover<3->{\node [white, above=0.05cm of third] (thirteen) {{working directory of PALM user}};}
+      \uncover<5->{\node [white, above=0.05cm of fifth] (fourteen) {{contains job protocol files from batch jobs}};}
+      \uncover<6->{\node [white, below=0.05cm of sixth] (fifteen) {{older PALM version, if needed}};}
+      \uncover<7->{\node [white1, right=0.2cm of seventh] (sixteen) {{parameter files for steering, output data}};}
+      \uncover<8->{\node [white1, right=0.2cm of eighth] (seventeen) {{code extensions from user (user interface)}};}
+      \uncover<4->{\node [white1, right=0.2cm of fourth] (eighteen) {{PALM software (FORTRAN code, scripts, etc.) }};}
+      \uncover<9->{\node [white1, right=0.2cm of ninth] (nineteen) {{precompiled routines, generated by \textbf{mbuild}}};}
+      \uncover<10->{\node [white1, right=0.2cm of tenth] (twenty) {{$\ldots$ compiled with different options (e.g. for debugging)}};}
+      \uncover<11->{\node [white1, right=0.2cm of eleventh] (twentyone) {{contains temporary directory created (by \textbf{mrun}) for each PALM run}};}
+      \uncover<12->{\node [white1, right=0.2cm of twelfth] (twentytwo) {{contains large binary data files created by PALM and needed e.g. for restarts}};}
+      \uncover<5->{\node [white1, below=1cm of tenth] (twentythree) {{}};}
+      \uncover<5->{\node [white, right=1cm of twentythree] (twentyfour) {{optional}};}
+      \uncover<4->{\node [white, above=0.1cm of eighteen] (twentyfifth) {{}};}
+      \uncover<4->{\node [white, below=0.1cm of eighteen] (twentysixth) {{}};}
+      \uncover<7->{\node [white, above=0.1cm of sixteen] (twentyseventh) {{}};}
+      \uncover<7->{\node [white, below=0.1cm of sixteen] (twentyeighth) {{}};}
+
+      \path<2-> [line] (first.east) -- (second.west);
+      \path<3-> [line] (second.east) -- (third.west);
+      \path<4-> [line] (third.east) -- (fourth.west);
+      \path<4-> [line] (fourth.east) -- (twentyfifth.west);
+      \path<4-> [line] (fourth.east) -- (twentysixth.west);
+      \path<4-> [line] (fourth.east) -- (eighteen.west);
+      \path<5-> [line,dashed] (first.east) -- (fifth.west);
+      \path<5-> [line,dashed] (twentythree.east) -- (twentyfour.west);
+      \path<6-> [line,dashed] (second.east) -- (sixth.west);
+      \path<7-> [line] (third.east) -- (seventh.west);
+      \path<7-> [line] (seventh.east) -- (twentyseventh.west);
+      \path<7-> [line] (seventh.east) -- (twentyeighth.west);
+      \path<7-> [line] (seventh.east) -- (sixteen.west);
+      \path<8-> [line] (eighth.east) -- (twentyfifth.west);
+      \path<8-> [line] (eighth.east) -- (twentyeighth.west);
+      \path<8-> [line,dashed] (third.east) -- (eighth.west);
+      \path<8-> [line] (eighth.east) -- (seventeen.west);
+      \path<9-> [line] (third.east) -- (ninth.west);
+      \path<10-> [line,dashed] (third.east) -- (tenth.west);	
+   \end{tikzpicture}
+\end{frame}
+
+%Folie 13
+\begin{frame}
+   \frametitle{PALM - Main Modes of Operation}
+   \begin{itemize}
+      \item<1->{\textbf{Interactive mode}}
+      \begin{itemize}
+         \item<2->{PALM is run in interactive shell (terminal session)}
+         \item<3->{CPU time as well as number of processors for interactive runs is limited on many systems}
+         \item<4->{restart runs (job chain) are not possible}
+         \item<5->{only requires appropriate settings in the configuration file}
+      \end{itemize}
+      \item<6->\textbf{{Batch mode (running batch jobs)}}
+      \begin{itemize}
+         \item<7->{requires a batch queueing system (e.g. NQS, PBS, Loadleveler, etc.) on the computer in use}
+         \item<8->{still may require manual adjustments of PALM scripts (\textbf{mrun, mbuild, subjob})}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+%Folie 14
+\begin{frame}
+   \begin{itemize}	
+      \item<1->{\textbf{Running batch jobs on remote computers}}
+      \begin{itemize}
+         \item<2->{requires a batch queueing system on the remote computer}
+         \item<3->{requires ssh/scp access of the remote computer (in both directions âlocal $\leftrightarrow$ remoteâ),
+                   fixed IP-adresses for local and remote computer are required}
+      \end{itemize}
+      \item<4->\textbf{{Running job chains}}
+      \begin{itemize}
+         \item<5->{requires a batch queueing system (+ ssh/scp access)}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+%Folie 15
+\begin{frame}
+   \frametitle{PALM - Scripts for Operating}
+   {\scriptsize PALM is operated by two scripts, named \textbf{mbuild} and \textbf{mrun}. \textbf{mrun} itself calls some helper programs and, if a batch job is to be submitted, the script \textbf{subjob}.}
+   \begin{itemize}
+      \item<2->{\textbf{mrun}}
+      \begin{itemize}
+         \item<3->{{\scriptsize script for running PALM (interactive or batch)}}
+      \end{itemize}
+      \item<4->{\textbf{mbuild}}
+      \begin{itemize}
+         \item<5->{{\scriptsize script for generating a pre-compiled PALM version (object files)}}
+      \end{itemize}
+      \item<6->{\textbf{subjob}}
+      \begin{itemize}
+         \item<7->{{\scriptsize script for generating an submitting batch jobs}}
+      \end{itemize}
+      \item<8->{\textbf{helper programs}}
+      \begin{itemize}
+         \item<9->{{\scriptsize small FORTRAN programs, needed e.g. for interpreting the configuration file and for collecting output data (\texttt{interpret-config.x}, \texttt{combine-plot-fields.x})}}
+      \end{itemize}
+   \end{itemize}
+
+   \tikzstyle{white} = [rectangle, text width=0.25\textwidth, font=\scriptsize]
+   \tikzstyle{white1} = [rectangle, text width=0.95\textwidth, font=\scriptsize]
+   \tikzstyle{line} = [draw, -]
+   \tikzstyle{green} = [rectangle, draw, fill=green!20, text width=0.15\textwidth, font=\scriptsize]
+
+   \begin{tikzpicture}[auto, node distance=0]
+      \uncover<10->{\node [white] (first) {{Location of scripts:}};}
+      \uncover<11->{\node [green, right=0.5cm of first] (second) {\textbf{trunk/} };}	
+      \uncover<11->{\node [white, right=0.5cm of second] (third) {{}};}
+      \uncover<11->{\node [green, below=0.15cm of third] (fourth) {\textbf{SCRIPTS/}};}
+      \path<11-> [line] (second.east) -- (fourth.west);
+      \uncover<11->{\node [white1, below=0.65cm of second] (fifth) {{The scripts have a large number of options. A short summary of available options can be listed by giving the question mark as the only option, e.g.  \texttt{mrun ?}}};}
+   \end{tikzpicture}
+\end{frame}
+
+%Folie 16
+\begin{frame}
+   \frametitle{PALM - Configuration File}
+   {\scriptsize \textbf{mrun and mbuild} require a lot of settings (which depend on the respective computer system used), which have to be given in a configuration file with default name  \texttt{.mrun.config}}\\
+   \begin{itemize}
+      \item<1->{\textbf{Main purposes of the configuration file:}}
+      \begin{itemize}
+         \item<2->{setting of compiler options}
+         \item<3->{setting of paths for libraries (e.g. netCDF library)}
+         \item<4->{setting of environment variables}
+         \item<5->{definition of (UNIX-)commands to be executed before or after PALM execution}
+         \item<6->{handling of input/output files by file connection statements}
+      \end{itemize}
+   \end{itemize}
+
+   \tikzstyle{white} = [rectangle, text width=0.3\textwidth, font=\scriptsize]
+   \tikzstyle{yellow} = [rectangle, draw, fill=yellow!20, text width=0.2\textwidth, font=\scriptsize]
+   \tikzstyle{line} = [draw, -]
+   \tikzstyle{green} = [rectangle, draw, fill=green!20, text width=0.2\textwidth, font=\scriptsize]
+
+   \begin{tikzpicture}[auto, node distance=0]
+      \uncover<7->{\node [white] (first) {{Default position for \\\texttt{.mrun.config}:}};}
+      \uncover<8->{\node [yellow, right=0.2cm of first] (second) {\textbf{home/} };}
+      \uncover<9->{\node [yellow, right=0.25cm of second] (third) {\textbf{palm/}};}
+      \uncover<10->{\node [yellow, right=0.25cm of third] (fourth) {\textbf{current-version/}};}
+      \path<9-> [line] (second.east) -- (third.west);
+      \path<10-> [line] (third.east) -- (fourth.west);
+      \uncover<11->{\node [white, below=0.15cm of first] (fifth) {{A default version of this file \texttt{.mrun.config.default} \\(to be adjusted by the user) can be found in:}};}
+      \uncover<12->{\node [green, below=0.35cm of second] (sixth) {\textbf{trunk/}};}
+      \uncover<13->{\node [green, below=0.7cm of third] (seventh) {\textbf{SCRIPTS/}};}
+      \path<13-> [line] (sixth.east) -- (seventh.west);
+   \end{tikzpicture}	
+\end{frame}
+
+%Folie 17
+\begin{frame}
+   \frametitle{PALM - Other Requirements for Running}
+
+   \tikzstyle{alert} = [rectangle, draw, text width=0.8\textwidth, font=\scriptsize]
+
+   \begin{tikzpicture}[auto, node distance=0]
+      \uncover<2->{\node [alert] (first) {\textbf{The following things are not provided with the download!}};}
+   \end{tikzpicture}
+
+   \begin{itemize}
+      \item<3->{Korn-Shell (/bin/ksh), either AT and T or public domain}
+      \item<4->{subversion, a version control system (www.tigris.org)}
+      \begin{itemize}
+         \item<5->{needed for downloading the PALM code}
+      \end{itemize}
+      \item<6->{FORTRAN 90/95 compiler}
+      \item<7->{MPI-library (must fit to the compiler!), MPI-2 not required}
+      \item<8->{netCDF-library (see www.unidata.ucar.edu/software/netcdf/)}
+      \begin{itemize}
+         \item<9->{needed for data output}
+      \end{itemize}
+      \item<10->{graphics software capable to read netCDF data format}
+      \begin{itemize}
+         \item<11->{e.g. NCL, IDL, ferret}
+      \end{itemize}
+      \item<12->{Batch-system}
+      \item<13->{ssh/scp connection to the remote host (both ways)}
+   \end{itemize}
+\end{frame}
+
+\end{document}
Index: palm/trunk/TUTORIAL/SOURCE/program_control.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/program_control.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/program_control.tex	(revision 915)
@@ -0,0 +1,345 @@
+% $Id$
+\input{header_tmp.tex}
+%\input{header_lectures.tex}
+
+\usepackage[utf8]{inputenc}
+\usepackage{ngerman}
+\usepackage{pgf}
+\usetheme{Dresden}
+\usepackage{subfigure}
+\usepackage{units}
+\usepackage{multimedia}
+\usepackage{hyperref}
+\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
+\usepackage{xmpmulti}
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows,positioning,decorations.pathreplacing}
+\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+
+%---------- neue Pakete
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{multicol}
+\usepackage{pdfcomment}
+
+\institute{Institut fÃŒr Meteorologie und Klimatologie, Leibniz UniversitÃ€t Hannover}
+\date{last update: \today}
+\event{PALM Seminar}
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamertemplate{footline}
+  {%
+    \begin{beamercolorbox}[rightskip=-0.1cm]&
+     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
+      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
+      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
+    \end{beamercolorbox}%
+%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
+%    \end{beamercolorbox}
+  }%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.eps}}
+
+\title[Program Control by Physical Parameters]{Program Control by Physical Parameters}
+\author{Siegfried Raasch}
+
+% Notes:
+% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
+% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
+\begin{document}
+
+\begin{frame}
+\titlepage
+\end{frame}
+
+% Folie 1
+\begin{frame}
+   \frametitle{Steering of PALM and Interpreting the Output}
+   \begin{itemize}
+      \item<1->{This section section describes how to steer the model and how to interpret the model output (\textbf{it does not explain, how to start and control model runs}).}
+      \item<2->{It gives a general overview of the input and output files and explaines the contents of the most important files in some detail.}
+   \end{itemize}
+\end{frame}
+
+% Folie 2
+
+\begin{frame}
+   \frametitle{PALM Input/Output Overview (I)}
+   \tikzstyle{start} = [ellipse, draw, fill=green!20, font=\small]   
+   \tikzstyle{yellow1} = [rectangle, draw, fill=yellow!20, text width=0.2\textwidth, font=\Tiny]
+   \tikzstyle{yellow2} = [rectangle, draw, fill=yellow!20, text width=0.1\textwidth, font=\Tiny]
+   \tikzstyle{yellow3} = [rectangle, draw, fill=yellow!20, text width=0.03\textwidth, font=\Tiny]
+   \tikzstyle{red} = [rectangle, draw, fill=red!100, text width=0.1\textwidth, font=\Tiny]
+   \tikzstyle{red2} = [rectangle, draw, fill=red!100, text width=0.03\textwidth, font=\Tiny]
+   \tikzstyle{orange1} = [rectangle, draw, fill=orange!50, text width=0.1\textwidth, font=\Tiny]
+   \tikzstyle{orange2} = [rectangle, draw, fill=orange!50, text width=0.11\textwidth, font=\Tiny]
+   \tikzstyle{orange3} = [rectangle, draw, fill=orange!50, text width=0.03\textwidth, font=\Tiny]
+
+   \tikzstyle{line} = [draw, -latex']
+   
+   \begin{tikzpicture} [auto]
+    \node[start] (palm) {\textbf{PALM}}; 
+
+    \uncover<2->{\node[yellow1] (parameterfile) [above left=1.5cm of palm] {parameter file \\ for steering};}
+    \uncover<6->{\node[red] (restartdata1) [above right=1.8cm of palm] {restart data};}
+    \uncover<5->{\node[red] (restartdata2) [below=4.5cm of restartdata1] {restart data};}
+
+    \uncover<3->{\node[yellow1] (runcontrol) [below=1.0cm of palm]{run control output\\ (parameter settings + \\ timestep informations)};}
+    \uncover<3->{\node[yellow2] (headerfile) [left=0.5cm of runcontrol]{header file};}
+    \uncover<3->{\node[yellow2] (cpumeasure) [left=0.5cm of headerfile]{cpu\\ measurements};}
+
+    \uncover<4->{\node[orange1] (1dmean) [below=0.5cm of cpumeasure] {1D mean \\ profiles};
+    \node[orange1] (2dsections) [right=0.5cm of 1dmean] {2D sections};
+    \node[orange1] (3ddata) [right=0.5cm of 2dsections] {3D data};
+
+    \node[orange1] (timeseries) [below=0.2cm of 1dmean] {time series};
+    \node[orange2] (2dsectionstime) [right=0.5cm of timeseries] {2D sections \\ time averaged};
+    \node[orange2] (3ddatatime) [right=0.39cm of 2dsectionstime] {3D data \\ time averaged};}
+
+    \node (program) [right=3.1cm of palm] {program};
+    \uncover<2->{\node (steeringdata) [right=0.6cm of restartdata1] {steering data};}
+    \uncover<3->{\node (run) [right=2.5cm of runcontrol] {run informations};}
+    \uncover<4->{\node (analysis) [right=3.6cm of 3ddata] {analysis data};}
+
+    \uncover<7->{
+    \node[yellow3] (yellow) [below=0.5 of timeseries] {};
+    \node (ascii) [right=0.1cm of yellow] {ASCII};
+    \node[orange3] (orange) [right=0.4cm of ascii] {};
+    \node (netcdf) [right=0.1cm of orange] {netCDF};
+    \node[red2] (red) [right=0.4cm of netcdf] {};
+    \node (binary) [right=0.1cm of red] {binary};}
+
+    \path<2->[line] (parameterfile) -- (palm);
+    \path<3->[line] (palm) -- (cpumeasure);
+    \path<3->[line] (palm) -- (headerfile);
+    \path<3->[line] (palm) -- (runcontrol);
+    \path<4->[line] (palm) -- (1dmean);
+    \path<4->[line] (palm) -- (2dsections);
+    \path<4->[line] (palm) -- (3ddata);
+    \path<4->[line] (palm) -- (timeseries);
+    \path<4->[line] (palm) -- (2dsectionstime);
+    \path<4->[line] (palm) -- (3ddatatime);
+    \path<5->[line] (palm) -- (restartdata2);
+    \path<6->[line] (restartdata1) -- (palm);
+    \path<6->[line,dashed] (restartdata2) -- (restartdata1);    
+   \end{tikzpicture}
+\end{frame}
+
+% Folie 3
+\begin{frame}
+   \frametitle{PALM Input/Output Overview (I)}
+   \tikzstyle{start} = [ellipse, draw, fill=green!20, font=\small]   
+   \tikzstyle{yellow1} = [rectangle, draw, fill=yellow!20, text width=0.2\textwidth, font=\Tiny]
+   \tikzstyle{yellow2} = [rectangle, draw, fill=yellow!20, text width=0.1\textwidth, font=\Tiny]
+   \tikzstyle{yellow3} = [rectangle, draw, fill=yellow!20, text width=0.03\textwidth, font=\Tiny]
+   \tikzstyle{yellow4} = [rectangle, draw, fill=yellow!100, text width=1.8cm, font=\Tiny]
+   \tikzstyle{red} = [rectangle, draw, fill=red!100, text width=0.1\textwidth, font=\Tiny]
+   \tikzstyle{red2} = [rectangle, draw, fill=red!100, text width=0.03\textwidth, font=\Tiny]
+   \tikzstyle{orange1} = [rectangle, draw, fill=orange!50, text width=0.1\textwidth, font=\Tiny]
+   \tikzstyle{orange2} = [rectangle, draw, fill=orange!50, text width=0.11\textwidth, font=\Tiny]
+   \tikzstyle{orange3} = [rectangle, draw, fill=orange!50, text width=0.03\textwidth, font=\Tiny]
+
+   \tikzstyle{line} = [draw, -]
+   
+   \begin{tikzpicture} [auto]
+    \node[start] (palm) {\textbf{PALM}}; 
+
+    \node[yellow1] (parameterfile) [above left=1cm of palm] {parameter file \\ for steering};
+    \node[red] (restartdata1) [above right=1.3cm of palm] {restart data};
+    \node[red] (restartdata2) [below=2.5cm of restartdata1] {restart data};
+
+    \node[yellow1] (runcontrol) [below=0.4cm of palm]{run control output\\ (parameter settings + \\ timestep informations)};
+    \node[yellow2] (headerfile) [left=0.5cm of runcontrol]{header file};
+    \node[yellow2] (cpumeasure) [left=0.5cm of headerfile]{cpu\\ measurements};
+
+    \node[orange1] (1dmean) [below=0.3cm of cpumeasure] {1D mean \\ profiles};
+    \node[orange1] (2dsections) [right=0.5cm of 1dmean] {2D sections};
+    \node[orange1] (3ddata) [right=0.5cm of 2dsections] {3D data};
+
+    \node[orange1] (timeseries) [below=0.2cm of 1dmean] {time series};
+    \node[orange2] (2dsectionstime) [right=0.5cm of timeseries] {2D sections \\ time averaged};
+    \node[orange2] (3ddatatime) [right=0.39cm of 2dsectionstime] {3D data \\ time averaged};
+
+    \node (program) [right=3.1cm of palm] {program};
+    \node (steeringdata) [right=0.6cm of restartdata1] {steering data};
+    \node (run) [right=2.5cm of runcontrol] {run informations};
+    \node (analysis) [right=3.6cm of 3ddata] {analysis data};
+    
+    \node[yellow3] (yellow) [below=0.3 of timeseries] {};
+    \node (ascii) [right=0.1cm of yellow] {ASCII};
+    \node[orange3] (orange) [right=0.4cm of ascii] {};
+    \node (netcdf) [right=0.1cm of orange] {netCDF};
+    \node[red2] (red) [right=0.4cm of netcdf] {};
+    \node (binary) [right=0.1cm of red] {binary};
+
+    %--------- neue Ordner
+    \node[yellow4] (currentversion) [above=0.6cm of parameterfile] {current\_version/};
+    \node[yellow4] (jobs) [right=0.3cm of currentversion] {JOBS/};
+    \node[yellow4] (runidentifier) [right=0.4cm of jobs] {\textless run\_identifier \textgreater/};
+    \node[yellow4] (input) [above right=1cm of runidentifier] {INPUT/};
+    \node[yellow4] (monitoring) [below=0.1cm of input] {MONITORING/};
+    \node[yellow4] (output) [below=0.1cm of monitoring] {OUTPUT/};
+    \node[yellow4] (restart) [below=0.1cm of output] {RESTART\_DATA/};
+
+    \node[yellow4] (input2) [below=0.1cm of parameterfile] {INPUT/};
+    \node[yellow4] (monitoring2) [above=0.6cm of headerfile] {MONITORING/};
+    \node[yellow4] (restart2) [below=0.1cm of restartdata1] {RESTART\_DATA/};
+    \node[yellow4] (tmpdata) [below=0.1cm of restart2] {/tmp\_data\_catalog/};
+    \node[yellow4] (output2) [below=0.5cm of restartdata2] {OUTPUT/};
+
+    \path[line] (currentversion) -- (jobs);
+    \path[line] (jobs) -- (runidentifier);
+    \path[line] (runidentifier.east) -- (input.west);
+    \path[line] (runidentifier.east) -- (monitoring.west);
+    \path[line] (runidentifier.east) -- (output.west);
+    \path[line] (runidentifier.east) -- (restart.west);
+
+    \draw[decorate,decoration={brace,raise=6pt,amplitude=9pt},thick]
+       (-4.5,-0.95)--(-1,-0.95) ;
+    \draw[decorate,decoration={brace,mirror,raise=5pt,amplitude=6pt},thick]
+       (0.45,-3)--(0.45,-1.9) ;
+
+
+%     \path[line] (monitoring2.south) -- (cpumeasure.north);
+%     \path[line] (monitoring2.south) -- (headerfile.north);
+%     \path[line] (monitoring2.south) -- (runcontrol.north);
+   
+   \end{tikzpicture}
+\end{frame}
+
+%---------------------------------------------------
+\begin{frame}
+   \frametitle{The Parameter File}
+   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\tiny]
+   \footnotesize
+   \begin{itemize}
+      \item{Physical and numerical features of a PALM run (e.g. initial and boundary conditions, numerical methods)
+            are controlled by a so called \textbf{parameter file} which uses FORTRAN-NAMELIST syntax.} 
+      \item{General structure of a FORTRAN-NAMELIST file}
+   \end{itemize}   
+   \begin{tikzpicture}[auto]      
+      \node[box](firstbox){ \begin{tabbing}        
+         \&abcd \quad \=no\_of\_eggs = 100, litres\_of\_milk = 50.0, \= \\
+                 \>kilos\_of\_butter = 20.0, \> /  \end{tabbing}};       
+   \end{tikzpicture}
+   \begin{itemize}
+      \item{This file can be read from a FORTRAN program in the following way:} 
+   \end{itemize}
+   \begin{tikzpicture}[auto, node distance=0]      
+      \node[box](secondbox){ \begin{tabbing} 
+         INTEGER :: \=no\_of\_eggs = 30 \\
+         REAL :: \> litres\_of\_milk = 0.0, kilos\_of\_butter, kilos\_of\_cream = 33.0 \\
+         NAMELIST /abcd/ \quad no\_of\_eggs, litres\_of\_milk, kilos\_of\_butter, kilos\_of\_cream \\
+         \par\bigskip
+         OPEN ( 1, FILE='Filename' ) \\
+         READ ( 1, abcd ) \end{tabbing}};       
+   \end{tikzpicture}
+   \normalsize 
+\end{frame}
+
+
+%-----------------------------------------------------
+\begin{frame}
+   \frametitle{The Run Control File}
+   \scriptsize
+   \begin{itemize}
+      \item{For initial runs, the parameter settings and many additional informations about the run (header informations) are printed at the beginning of this file.}
+      \item<2->{The parameter settings are followed by values of specific model variables for certain timesteps (one line for each timestep, the output intervall can be
+            controlled by run parameter {\tt dt\_run\_control}).}
+   \end{itemize}
+   \onslide<3->{
+   \textbf{Contents of this timestep output should be carefully checked after each run, because it allows a first control, if the model had run correctly, or if any
+           errors have occurred!}}
+   \includegraphics[width=1.6\textwidth]{program_control_figures/run_control_file.png}
+   \normalsize
+\end{frame}
+
+%-----------------------------------------------------
+\begin{frame}
+   \frametitle{The Header File}
+   \scriptsize
+   \begin{itemize}
+      \item{The header file contains nearly the same informations as the header of the run control file of the initial run.} 
+      \item<2->{It is generated for \textbf{every} run (initial run as well as restart runs).}
+      \item<3->{It is created at the beginning \textbf{and} at the end of a run (overwrites the file created at beginning).}
+      \item<4->{Only at the end, cpu time information is included!}
+   \end{itemize}
+   \begin{center}
+   \includegraphics[width=0.9\textwidth]{program_control_figures/header_file.png}
+   \end{center}
+   \normalsize
+\end{frame}
+
+%-------------------------------
+\begin{frame}
+   \frametitle{CPU Measurements File}
+   \begin{columns}[c]
+   \column{0.42\textwidth}
+      \scriptsize
+      \begin{itemize}
+         \item{Contains informations about the CPU requirements of single parts of the program.}
+         \item<2->{It should be inspected regularly in order to find out, if the code is still well optimized (e.g. load balance).} 
+         \item<3->{Prognostic-equations and pressure solver ({\tt pres}) should be the main consumer.}
+         \item<4->{For larger grids ($400^3$ points), {\tt pres} may need up to 50\% of the total time.}
+         \item<5->{Time needed for communication (sum of {\tt exchange\_horiz}({\tt \_2d}) and {\tt mpi\_alltoall}) should not exceed about 10-15\% of the total time.}
+      \end{itemize}
+      \normalsize
+   \column{0.58\textwidth}
+      \includegraphics[width=\textwidth]{program_control_figures/cpu_measurements_file.png}
+   \end{columns}
+\end{frame}
+
+%-----------------------------------------------------
+\begin{frame}
+   \frametitle{Other Files}
+   \begin{itemize}
+      \item<1->{Data output files (1D profiles and timeseries, 2D cross sections, 3D volume data) are by default in \textbf{netCDF} format which is suitable to be processed by
+            public domain graphics software like \textbf{ncview}, \textbf{ferret}, \textbf{ncl} (used by PALM group),\\
+            \textbf{IDL}, etc. \\
+            For a first look, {\tt ncview} is a convenient tool.}
+      \item<2->{{\tt ncdump} can be used to display the netCDF file contents in ASCII format ({\tt ncdump -c} displays only header informations).}
+      \item<3->{The simple viewer for netCDF-data - {\tt ncview} - as well as ncl graphic software is available on the IMUK-cluster.}
+   \end{itemize}
+\end{frame}
+
+%----------------------------------------------------
+\begin{frame}
+   \frametitle{Steering by Unix Environment Variables}
+   \footnotesize
+   Most features of PALM are controlled by the parameter file but a few are exclusively controlled by unix environment variables. The most important one is  {\tt write\_binary}. \\
+   Setting \\
+   \begin{centering} {\tt write\_binary = true} \end{centering} \\
+   within the shell causes PALM to write binary data for restart runs at the end of a run.
+   
+   Setting of these environment variables is automatically done by  mrun. It generates a local file (named {\tt ENVPAR}) in FORTRAN-NAMELIST-format, which is then read by PALM. This file
+   includes the following variables: \\
+ 
+   \tiny
+   \begin{tabular}{|p{3cm}|p{5cm}|p{2cm}|} \hline
+      \textbf{Variable}                 & \textbf{Meaning} & \textbf{Value set by {\tt mrun}-option} \\
+      \hline
+      {\tt host}                        & host identifier that mrun is using for the host on which the job is running & {\tt -h}    \\
+      {\tt maximum\_cpu\_time\_allowed} & cpu time allowed for the job                                                & {\tt -t}    \\
+      {\tt run\_identifier}             & identification string for the run    & {\tt -d}    \\
+      {\tt tasks\_per\_node}            & number of MPI tasks to be started on each node     & {\tt -T}     \\
+      {\tt write\_binary}               & switch for writing binary data to be used for restart runs     & {\tt -r} (+setting in configuration file {\tt .mrun.config)}       \\
+      \hline
+   \end{tabular}
+   \normalsize
+\end{frame}
+
+%-----------------------------------------
+\begin{frame}
+   \frametitle{PALM / netCDF Documentation}
+   \begin{itemize}
+      \item<1->{A detailed description of how to use PALM and a complete list of steering parameters and their meaning can be found on the PALM-server: \\
+            \par\bigskip
+            \textbf{http://palm.muk.uni-hannover.de/wiki/doc/toc}}
+      \par\bigskip
+      \item<2->{General information about the netCDF data format can be found under \\
+            \par\bigskip
+            \textbf{http://www.unidata.ucar.edu/software/netcdf/}}
+   \end{itemize}
+\end{frame}
+
+\end{document}
Index: palm/trunk/TUTORIAL/SOURCE/sgs_models.tex
===================================================================
--- palm/trunk/TUTORIAL/SOURCE/sgs_models.tex	(revision 915)
+++ palm/trunk/TUTORIAL/SOURCE/sgs_models.tex	(revision 915)
@@ -0,0 +1,355 @@
+% $Id$
+\input{header_tmp.tex}
+%\input{header_lectures.tex}
+
+\usepackage[utf8]{inputenc}
+\usepackage{ngerman}
+\usepackage{pgf}
+\usetheme{Dresden}
+\usepackage{subfigure}
+\usepackage{units}
+\usepackage{multimedia}
+\usepackage{hyperref}
+\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
+\usepackage{xmpmulti}
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows,positioning}
+\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{multicol}
+\usepackage{float}
+
+\institute{Institut fÃŒr Meteorologie und Klimatologie, Leibniz UniversitÃ€t Hannover}
+\date{last update: \today}
+\event{PALM Seminar}
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamertemplate{footline}
+  {
+    \begin{beamercolorbox}[rightskip=-0.1cm]&
+     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,
+      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}
+      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}
+    \end{beamercolorbox}
+    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}
+    \end{beamercolorbox}
+  }
+%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}}
+
+\title[SGS Models]{SGS Models}
+\author{Siegfried Raasch}
+
+% Notes:
+% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
+% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
+\begin{document}
+
+% Folie 1
+\begin{frame}
+\titlepage
+\end{frame}
+
+
+\section{SGS Models}
+\subsection{SGS Models}
+
+% Folie 2
+\begin{frame}
+   \frametitle{SGS Models (I)}
+   \small
+   \begin{itemize}
+      \item<2->The SGS model has to parameterize the effect of the SGS motions (small-scale turbulence) on the large eddies (resolved-scale turbulence).
+      \item<3->Features of small-scale turbulence: local, isotropic, dissipative (inertial subrange)
+      \item<4->SGS stresses should depend on:
+      \begin{itemize}
+         \item local resolved-scale field \hspace{3mm} and / or
+         \item past history of the local fluid (via a PDE)
+      \end{itemize}
+      \item<5->Importance of the model depends on how much energy is contained in the subgrid-scales:
+      \begin{itemize}
+         \item $E_{SGS} / E < 50\%$: results relatively insensitive to the model, (but sensitive to the numerics, e.g. in case of upwind scheme)
+         \item $E_{SGS} / E = 1$: model more important 
+         \item<6->\textbf{If the large-scale eddies are not resolved, the SGS model and the LES will fail at all!} 
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+% Folie 3
+\begin{frame}
+   \frametitle{SGS Models (II)}
+   Requirements that a good SGS model must fulfill:
+   \begin{footnotesize}
+      \begin{itemize}
+         \item<2-> Represent interactions with small scales.
+         \item<3-> Provide adequate dissipation\\ (transport of energy from the resolved grid scales to the unresolved grid scales; the rate of dissipation $\varepsilon$ in this context is the flux of energy through the inertial subrange).
+         \item<4-> Dissipation rate must depend on the large scales of the flow rather than being imposed arbitrarily by the model. The SGS model must depend on the large-scale statistics and must be sufficiently flexible to adjust to changes in these statistics.
+         \item<5->In energy conserving codes (ideal for LES) the only way for TKE to leave the resolved modes is by the dissipation provided by the SGS model.
+         \item<6->\underline{The primary goal of an SGS model is to obtain correct statistics of the}\\ 
+         \underline{energy containing scales of motion.}
+      \end{itemize}
+   \end{footnotesize}
+\end{frame}
+
+% Folie 4
+\begin{frame}
+   \frametitle{SGS Models (III)}
+   \onslide<1-> All the above observation suggest the use of an eddy viscosity type SGS model:
+   \begin{footnotesize}
+      \begin{itemize}
+         \item<2-> Take idea from RANS modeling, introduce eddy viscosity $\nu_T$:
+         \begin{flalign*}
+            &\tau_{ki} = - \nu_T \left( \frac{\partial \overline{u_k}}{\partial x_i}+ \frac{\partial \overline{u_i}}{\partial x_k}\right) = -2 \nu_T \overline{S}_{ki}& \text{with} \hspace{3mm} \overline{S}_{ki} = \frac{1}{2} \left( \frac{\partial \overline{u_k}}{\partial x_i}+ \frac{\partial \overline{u_i}}{\partial x_k}\right)\\
+            & & \text{filtered strain rate tensor}
+         \end{flalign*}
+      \end{itemize}
+   \end{footnotesize}
+   \onslide<3->Now we need a model for the eddy viscosity:
+   \begin{footnotesize}
+      \begin{itemize}
+         \item<4-> Dimensionality of $\nu_T$ is $l^2/t$
+         \item<5-> Obvious choice: $\nu_T = Cql$ \hspace{5mm} (q, l: characterictic velocity / length scale)
+         \item<6-> Turbulence length scale is easy to define: largest size of the unresolved scales is $\Delta$ \hspace{10mm} $l = \Delta$
+         \item<7-> Velocity scale not obvious (smallest resolved scales, their size is of the order of the variation of velocity over one grid element)
+         \begin{flalign*}
+            &q = l \frac{\partial \overline{u}}{\partial x} = l \overline{S}& \text{for 3D: } \overline{S} = \sqrt{2 \overline{S}_{ki}\,\overline{S}_{ki}} \hspace{15mm} \\
+            & & \text{characterictic filtered rate of strain}\hspace{15mm}
+         \end{flalign*}
+      \end{itemize}
+   \end{footnotesize}
+\end{frame}
+
+
+\section{Smagorinsky Model}
+\subsection{The Smagorinsky Model}
+
+% Folie 5
+\begin{frame}
+   \frametitle{The Smagorinsky Model}
+   \onslide<2->Combine previous expressions to obtain:
+   \begin{equation*}
+      \nu_T = C \Delta^2 \overline{S} = (C_S \Delta)^2 \overline{S}
+   \end{equation*}
+   \onslide<3-> Model due to Smagorinsky (1963):
+   \begin{itemize}
+      \item<3-> Originally designed at NCAR for global weather modeling.
+      \item<4-> Can be derived in several ways: heuristically (above), from inertial range arguments (Lilly), from turbulence theories.
+      \item<5-> Constant predicted by all methods (based on theory, decay of isotropic turbulence): $C_S = \sqrt{C} \approx 0.2$
+   \end{itemize}
+\end{frame}
+
+% Folie 6
+\begin{frame}
+   \frametitle{The Smagorinsky Model: Performance}
+   \begin{itemize}
+      \item<2-> Predicts many flows reasonably well
+      \item<3-> Problems:
+      \begin{itemize}
+         \item<3-> Optimum parameter value varies with flow type:
+         \begin{itemize}
+            \item Isotropic turbulence: $C_S \approx 0.2$\\
+            \item Shear (channel) flows: $C_S \approx 0.065$
+         \end{itemize}
+         \item<4-> Length scale uncertain with anisotropic filter:
+         \begin{equation*}
+            (\Delta_x \Delta_y \Delta_z)^{1/3} \hspace{5mm} (\Delta_x + \Delta_y + \Delta_z)/3
+         \end{equation*}
+         \item<5-> Needs modification to account for:
+         \begin{itemize}
+            \item stratification: $C_S = F(Ri,...)$, $Ri$: Richardson number\\
+            \item near-wall region: $C_S = F(z+)$, $z+$: distance from wall
+         \end{itemize}
+      \end{itemize}
+   \end{itemize}
+\end{frame}
+
+
+\section{Deardoff Modification}
+\subsection{Deardoff Modification}
+
+% Folie 7
+\begin{frame}
+   \frametitle{Deardorff (1980) Modification (Used in PALM) (I)}
+   \footnotesize
+   \onslide<1->{
+      $ \nu_T = Cql = C_M \Lambda \sqrt{\bar{e}} $ \quad \textbf{with} \quad $ \bar{e} = \frac{\overline{u_i' u_i'}}{2} $ \quad \textbf{SGS-turbulent kinetic energy}}
+   \normalsize
+   \begin{itemize}
+      \item<2->{The SGS-TKE allows a much better estimation of the velocity scale for the SGS fluctuations and also contains information about the past history of the local fluid.}
+   \end{itemize} 
+   \onslide<3->{
+      $ C_M = const. = 0.1 $
+      \par\bigskip
+      \scriptsize
+      $ \Lambda = \begin{cases} min\left( 0.7 \cdot z, \Delta \right), & \textbf{unstable or neutral stratification} \\
+                          min\left( 0.7 \cdot z, \Delta, 0.76 \sqrt{\bar{e}} \left[ \frac{g}{\Theta_0} \frac{\partial \bar{\Theta}}{\partial z} \right]^{-1/2} \right), & \textbf{stable                             stratification} 
+                  \end{cases} $      
+      \normalsize
+      \par\bigskip
+      $ \Delta = \left( \Delta x \Delta y \Delta z \right)^{1/3} $ }
+\end{frame}
+
+% Folie 8
+\begin{frame}
+   \frametitle{Deardorff (1980) Modification (Used in PALM) (II)}
+   \begin{itemize}
+      \item{SGS-TKE from prognostic equation}
+   \end{itemize}
+   $ \frac{\partial \bar{e}}{\partial t} = -\bar{u_k} \frac{\partial \bar{e}}{\partial x_k} - \tau_{ki} \frac{\partial \bar{u_i}}{\partial x_k} + \frac{g}{\Theta_0} \overline{u_3'             \Theta'} - \frac{\partial}{\partial x_k} \left\{ \overline{u_k' \left( e' + \frac{\pi'}{\rho_0} \right)} \right\} - \epsilon $                                         
+   \par\bigskip                                        
+   $ \frac{\partial}{\partial x_k} \left[ \overline{u_k' \left( e' + \frac{\pi'}{\rho_0} \right)} \right] = - \frac{\partial}{\partial x_k} \nu_e \frac{\partial \bar{e}}{\partial x_k} $
+   \par\bigskip
+   $ \nu_e = 2 \nu_T $
+   \par\bigskip
+   $ \epsilon = C_{\epsilon} \frac{\bar{e}^{3/2}}{\Lambda} \qquad \qquad C_{\epsilon} = 0.19 + 0.74\frac{\Lambda}{\Delta} $
+\end{frame}
+
+% Folie 9
+\begin{frame}
+   \frametitle{Deardorff (1980) Modification (Used in PALM) (III)}
+   \begin{itemize}
+      \item{There are still problems with this parameterization:}
+      \begin{itemize}
+         \item[-]<2->{The model overestimates the velocity shear near the wall.}
+         \item[-]<3->{$\textrm{C}_\mathrm{M}$ is still a constant but actually varies for different types of flows.}
+         \item[-]<4->{Backscatter of energy from the SGS-turbulence to the resolved-scale flow can not be considered.}
+      \end{itemize}
+      \item<5->{Several other SGS models have been developed:}
+      \begin{itemize}
+         \item[-]<5->{Two part eddy viscosity model (Sullivan, et al.)}
+         \item[-]<6->{Scale similarity model (Bardina et al.)}
+         \item[-]<7->{Backscatter model (Mason)}
+      \end{itemize}
+      \item<8->{However, for fine grid resolutions ($\textrm{E}_\mathrm{SGS} << \ \textrm{E}$) LES results become almost independent
+               from the different models (Beare et al., 2006, BLM).}
+   \end{itemize} 
+\end{frame}
+
+
+\section{Summary / Important Points for Beginners}
+\subsection{Summary / Important Points for Beginners}
+
+% Folie 10
+\begin{frame}
+   \frametitle{Summary / Important Points for Beginners (I)}
+   \begin{columns}[c]
+   \column[T]{0.4\textwidth} 
+      \includegraphics<2-7>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_2.png}   
+      \includegraphics<8>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_8.png}
+      \includegraphics<9>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_9.png}
+      \includegraphics<10>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_10.png}
+      \onslide<8-10>{\begin{flushright} \begin{tiny} after Schatzmann and Leitl (2001) \end{tiny} \end{flushright}}              
+   \column[T]{0.2\textwidth}
+      \vspace{0.9cm}
+      \includegraphics<8-10>[width=0.7\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_arrow.png}
+      \par
+      \onslide<8->{\begin{small} fluctuations (\textbf{u},c) \end{small}}
+      \par\bigskip
+      \thicklines
+      \onslide<9->{\mbox{\line(6,0){5} \, \line(1,0){5} \, \line(1,0){5} \quad \begin{small} {critical concentration level} \end{small}}}
+      \vspace{1cm}
+      
+      \includegraphics<8-10>[width=0.7\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_arrow.png}
+      \par
+      \onslide<8->{\begin{small} smooth result \end{small}}   
+   \column[T]{0.4\textwidth}     
+      \includegraphics<1-2>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_1.png}
+      \includegraphics<3>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_3.png}
+      \includegraphics<4>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_4.png}
+      \includegraphics<5-10>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_5.png}
+      \vspace{1.3cm}
+      \includegraphics<6>[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_6.png}
+      \uncover<7->{\includegraphics[width=\textwidth]{sgs_models_figures/Important_Points/Important_Points_1_7.png}}       
+   \end{columns}
+\end{frame}
+
+% Folie 11
+\begin{frame}
+   \frametitle{Summary / Important Points for Beginners (II)}
+    For an LES it always has to be guaranteed that the main energy containing eddies of the respective 
+    turbulent flow can really be simulated by the numerical model:      
+    \begin{itemize}
+       \item<2->{The grid spacing has to be fine enough.}
+       \item<3->{$\textrm{E}_\mathrm{SGS} < (<<) \ \textrm{E} $}
+       \item<4->{The inflow/outflow boundaries must not effect the flow turbulence \\
+                (therefore cyclic boundary conditions are used in most cases).}
+       \item<5->{In case of homogeneous initial and boundary conditions, the onset of turbulence 
+                  has to be triggered by imposing random fluctuations.}
+       \item<6->{Simulations have to be run for a long time to reach a stationary state and stable statistics.}
+    \end{itemize}      
+\end{frame}
+
+
+\section{Example Output}
+\subsection{Example Output}
+
+% Folie 12
+\begin{frame}
+   \frametitle{Example Output (I)}
+   \begin{itemize}
+      \item{LES of a convective boundary layer}
+   \end{itemize}
+   \includegraphics<1>[width=\textwidth]{sgs_models_figures/Example_Output_1/Example_Output_1_1.png}
+   \includegraphics<2>[width=\textwidth]{sgs_models_figures/Example_Output_1/Example_Output_1_2.png}
+   \includegraphics<3>[width=\textwidth]{sgs_models_figures/Example_Output_1/Example_Output_1_3.png}
+   \includegraphics<4>[width=\textwidth]{sgs_models_figures/Example_Output_1/Example_Output_1_4.png}
+   \includegraphics<5>[width=\textwidth]{sgs_models_figures/Example_Output_1/Example_Output_1_5.png}
+   \includegraphics<6>[width=\textwidth]{sgs_models_figures/Example_Output_1/Example_Output_1_6.png}
+   \includegraphics<7>[width=\textwidth]{sgs_models_figures/Example_Output_1/Example_Output_1_7.png}
+\end{frame}
+
+% Folie 13
+\begin{frame}
+   \frametitle{Example Output (II)}
+   \begin{itemize}
+      \item{LES of a convective boundary layer}
+   \end{itemize}
+   \begin{center}
+      \includegraphics[width=0.8\textwidth]{sgs_models_figures/Example_output_2.png}
+      power spectrum of vertical velocity
+   \end{center}
+\end{frame}
+
+% Folie 14
+\begin{frame}
+   \frametitle{Some Symbols}
+   \begin{columns}[c]
+      \column{0.6\textwidth}
+      \begin{tabbing}
+      $u_i \quad (i = 1,2,3)$ \quad \= velocity components \\
+      $u,v,w$ \\ 
+
+      \\
+      
+      $x_i \quad (i = 1,2,3)$ \> spatial coordinates \\
+      $x,y,z$ \\
+
+      \\
+
+      $\Theta$ \> potential temperature \\ \\
+
+      $\Psi$ \> passive scalar \\ \\
+
+      $T$ \> actual Temperatur \\ \\
+      \end{tabbing}
+   \column{0.4\textwidth}
+      \begin{tabbing}
+      $\Phi = gz$  \quad \= geopotential \\ \\
+
+      $p$ \> pressure \\ \\
+
+      $\rho$ \> density \\ \\
+
+      $f_i$ \> Coriolis Parameter \\ \\
+
+      $\epsilon_{ijk}$ \> alternating symbol \\ \\
+
+      $\nu, \nu_\Psi$ \> molecular diffusivity \\ \\
+
+      $Q, Q_\Psi$ \> sources or sinks \\ \\
+      \end{tabbing}
+   \end{columns}
+\end{frame}
+\end{document}
