source: palm/trunk/TUTORIAL/SOURCE/non_cyclic_boundary_conditions.tex @ 925

Last change on this file since 925 was 915, checked in by maronga, 12 years ago

added first LaTeX source code for the new tutorial

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1% $Id: non_cyclic_boundary_conditions.tex 915 2012-05-30 15:11:11Z maronga $
2\input{header_tmp.tex}
3%\input{header_lectures.tex}
4
5\usepackage[utf8]{inputenc}
6\usepackage{ngerman}
7\usepackage{pgf}
8\usetheme{Dresden}
9\usepackage{subfigure}
10\usepackage{units}
11\usepackage{multimedia}
12\usepackage{hyperref}
13\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
14\usepackage{xmpmulti}
15\usepackage{tikz}
16\usetikzlibrary{shapes,arrows,positioning}
17\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
18
19%---------- neue Pakete
20\usepackage{amsmath}
21\usepackage{amssymb}
22\usepackage{multicol}
23\usepackage{pdfcomment}
24
25\institute{Institut fÌr Meteorologie und Klimatologie, Leibniz UniversitÀt Hannover}
26\date{last update: \today}
27\event{PALM Seminar}
28\setbeamertemplate{navigation symbols}{}
29
30\setbeamertemplate{footline}
31  {%
32    \begin{beamercolorbox}[rightskip=-0.1cm]&
33     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
34    \end{beamercolorbox}
35    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
36      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
37      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
38    \end{beamercolorbox}%
39%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
40%    \end{beamercolorbox}
41  }%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.eps}}
42
43\title[PALM - Using Non-Cyclic Boundary Conditions]{PALM - Using Non-Cyclic Boundary Conditions}
44\author{Siegfried Raasch}
45
46% Notes:
47% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
48% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
49\begin{document}
50
51% Folie 1
52\begin{frame}
53\titlepage
54\end{frame}
55
56% Folie 2
57\begin{frame}
58   \frametitle{Cyclic Horizontal Boundary Conditions}
59   In many cases, LES models are using cyclic horizontal boundary conditions.
60   \par\bigskip
61   \textbf{Why?}
62   \par\bigskip
63   \begin{itemize}
64      \item<2->{LES requires that the main energy containing eddies are resolved by the model.}
65      \item<3->{With cyclic boundary conditions, turbulence can freely develop and is not effected by the side walls (because there are no walls!).}
66      \item<4->{Non-cyclic boundary conditions give problems:}
67      \begin{itemize}
68         \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.}
69         \item<6->{At the outflow, a boundary condition is required which allows the eddies to freely leave the domain.}
70      \end{itemize}
71   \end{itemize}   
72\end{frame}
73
74%Folie 3
75\begin{frame}
76   \frametitle{Motivation for Non-Cyclic Boundary Conditions}
77   \footnotesize
78   The main motivation for non-cyclic boundary conditions are studies of isolated phenomena.
79   \begin{tabbing}
80   \uncover<2->{\textbf{Example:} \= Turbulence generated by a single obstacle. \\}                   
81                    \uncover<6->{ \> Cyclic boundary conditions along x would allow the generated turbulence\\
82                     \>  to enter the domain again, and so finally to modify the turbulence \\
83                     \>  on the leeward side of the building. \\ }     
84                     \\ 
85                     \uncover<9>{ \> This wouldn't be a simulation of a single building, but of an\\
86                     \> infinite row of buildings! \\  }
87   \end{tabbing}
88   \begin{center}
89   \includegraphics<3>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_1.png}
90   \includegraphics<4>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_2.png}
91   \includegraphics<5-6>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_3.png}
92   \includegraphics<7>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_4.png}
93   \uncover<8->{\begin{center} \includegraphics[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_5.png} \end{center}}
94   \end{center}
95   \normalsize
96\end{frame}
97
98% Folie 4
99\begin{frame}
100   \frametitle{Implications of Non-Cyclic Boundary Conditions}
101   \footnotesize
102   \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!}
103   \par\bigskip
104   \includegraphics<3>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_1.png}
105   \includegraphics<4>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_2.png}
106   \uncover<5->{\includegraphics[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_3.png}}
107   \par\bigskip
108   \onslide<6->{Flow internal turbulence may develop, but this may require a very long model domain.}
109   \par\bigskip
110   \includegraphics<7>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_4.png}
111   \includegraphics<8>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_5.png}
112   \uncover<9->{\includegraphics[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_6.png}}
113   \onslide<10->{There is a need to supply turbulence information at the inflow.}
114\end{frame}
115
116% Folie 5
117\begin{frame}
118   \frametitle{How to Create a Turbulent Inflow (I)}
119   Two methods:
120   \begin{itemize}
121      \item<2->{by a statistical model}
122      \item<3->{by recycling-method  (Lund et al., 1998)}
123   \end{itemize}
124   \includegraphics<4>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_1_neu.png}
125   \includegraphics<5>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_2_neu.png}
126   \includegraphics<6>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_3_neu.png}
127   \includegraphics<7>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_4_neu.png}
128   \includegraphics<8>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_5_neu.png}
129   \uncover<9->{\includegraphics[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_6.png}}
130   \par\bigskip
131   \uncover<10>{How do we get the initial turbulence in the recycle area? \\
132   If there is no turbulence, there is nothing to recycle!}
133\end{frame}
134
135%Folie 6
136\begin{frame}
137   \frametitle{How to Create a Turbulent Inflow (II)}
138   \small
139   Initial  turbulence is created by a precursor run with cyclic boundary conditions and much smaller domain size than used for the main run.
140   \tikzstyle{line} = [draw, yellow, thick, dashed, -latex']   
141   \begin{tikzpicture}     
142      \uncover<1>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_1.png}};}
143      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_2.png}};}
144      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_3.png}};}
145      \node(text) [right=0.1cm of picture]{
146         \parbox{5cm}{
147         \scriptsize
148         \begin{itemize}
149         \item<4->{When the precursor run is finished, data of the last timestep are stored on disc.}
150         \item<5->{These data are then read by the main run and repeatedly mapped to the main run domain, unless it is completely filled.}
151         \end{itemize}}};
152     \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}};}
153     \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}};}
154     \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}};}
155     \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}};} 
156     \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}};} 
157     \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}};} 
158    \path<7->[line] (-0.45,-1) -- (-0.7,-2.6);
159    \path<7->[line] (1.78,-1) -- (1.68,-2.6); 
160    \path<8->[line] (-0.45,-1) -- (1.68,-2.6);
161    \path<8->[line] (1.78,-1) -- (4,-2.6);
162    \path<9->[line] (-0.45,-1) -- (4,-2.6);
163    \path<9->[line] (1.78,-1) -- (6.4,-2.6);
164    \path<10->[line] (-0.45,-1) -- (6.4,-2.6);
165    \path<10->[line] (1.78,-1) -- (6.9,-2.6);
166   \end{tikzpicture} 
167\end{frame}
168
169% Folie 7
170\begin{frame}
171   \frametitle{How to Create a Turbulent Inflow (III)}
172   \footnotesize
173   \begin{itemize}
174      \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
175            the last time step of the precursor run.}
176   \end{itemize}
177   \tikzstyle{line1} = [draw, red, thick, -latex']
178   \tikzstyle{line2} = [draw, red, thick, -]
179   \begin{tikzpicture}
180      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_1.png}};}
181      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_2.png}};}
182      \node(text) [right=0.1cm of picture]{
183         \parbox{6.5cm}{
184         \scriptsize
185         \begin{itemize}
186         \item<6->{Since the height of the turbulent boundary layer may increase with increasing distance from the inflow boundary, recycling has
187               to be limited to the height of the turbulent boundary layer at the inflow. Otherwise, the boundary layer height will continuously increase with time.}
188         \end{itemize}}};
189   \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}};}
190   \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}};}
191   \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}};}
192   \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}};}
193   \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}};}
194     
195   \path<5->[line2] (picture.east) -- (2.25,-1.3);
196   \path<5->[line2] (2.25,-1.3)    -- (-1.2,-1.3);
197   \path<5->[line2] (-1.2,-1.3)    -- (-1.2,-3.2);
198   \path<5->[line1] (-1.2,-3.2)      -- (-0.8,-3.2);
199   \end{tikzpicture}
200\end{frame}
201
202% Folie 8
203\begin{frame}
204   \frametitle{Non-Cyclic Boundary Conditions in PALM (I)}
205   \textbf{Status of availability:}
206   \begin{itemize}
207      \item<2->{Non-cyclic boundary conditions along \textbf{one} of the horizontal directions (x \textbf{or} y).}
208      \begin{itemize}
209         \item<3->{Dirichlet conditions at inflow (stationary vertical profiles, u(z), v(z), pt(z), q(z), w=0).}
210         \item<4->{Radiation conditions at outflow. Tendencies at the boundary are replaced by e.g.}
211      \end{itemize}     
212      \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} 
213                     \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}}
214      \par\bigskip
215      \item<5->{Turbulence recycling method for inflow \textbf{from left}.}
216   \end{itemize} 
217\end{frame}
218
219% Folie 9
220\begin{frame}
221   \frametitle{Non-Cyclic Boundary Conditions in PALM (II)}
222   \par\bigskip
223   \small
224   \textbf{Further requirements for PALM runs using non-cyclic boundary conditions:}
225   \par\bigskip
226   \begin{itemize}
227      \item<2->{The \textbf{multigrid-method} has to be used for solving the Poisson-equation.}
228      \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.}
229      \item<4->{\textbf{Volume flow conservation} should be activated, because otherwise flow acceleration or deceleration may occur along the non-cyclic direction.}
230      \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
231                inflow throughout the whole run, in order to maintain a turbulent state of the flow.}
232   \end{itemize}
233   \normalsize
234\end{frame}
235
236% Folie 10
237\begin{frame}
238   \frametitle{Current Applications of Non-Cyclic BCs (I)}
239   \textbf{Cold air outbreaks}
240   \par\bigskip
241   \includegraphics[width=\textwidth]{non_cyclic_figures/cold_air_outbreaks.png} \\
242   \par\bigskip
243   \tiny
244   \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.,
245   \textbf{35}, L23804, doi:10.1029/2008GL035845. \\
246   \par\bigskip
247   \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,
248    doi:10.1029/2005GL022872. \\
249   \normalsize
250   \begin{center} \uncover<2->{\textbf{Turbulence recycling has not been used!}} \end{center}
251\end{frame}
252
253% Folie 11
254\begin{frame}
255   \frametitle{Current Applications of Non-Cyclic BCs (II)}
256   \textbf{Cold air outbreaks}
257   \begin{center} 
258   \includegraphics[width=0.85\textwidth]{non_cyclic_figures/cold_air_outbreaks_2.png} \\
259   liquid water content (vertically intgrated) 
260   \end{center}
261\end{frame}
262
263% Folie 12
264\begin{frame}
265   \frametitle{How to set up non-cyclic runs with PALM}
266   \begin{itemize}
267      \item{\textbf{required} / recommended parameter settings:}
268   \end{itemize}
269   \par\bigskip
270   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
271   \begin{tikzpicture}     
272      \node[box](inipar){ \begin{tabbing} 
273         \&inipar \= ....... \\
274                  \\
275                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, (bc\_ns = 'dirichlet/radiation',) \\ 
276                  \> \textbf{psolver = 'multigrid'}, \\
277                  \\
278                  \> initializing\_actions = 'set\_1d-model\_profiles', \\
279                  \> conserve\_volume\_flow = .T., \\
280                  \\
281                  \> ...... / \\ \end{tabbing}};
282   \end{tikzpicture}
283\end{frame}
284
285% Folie 13
286\begin{frame}
287   \frametitle{How to set up turbulence recycling with PALM (I)}
288   \small
289   \begin{itemize}
290      \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.}
291      \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.
292                This enables writing of profiles to the restart file, which can then be used by the main run.}
293   \end{itemize}
294   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
295   \onslide<2->{
296   \begin{tikzpicture}     
297      \node[box](inipar){ \begin{tabbing} 
298         \&d3par \= end\_time = 3600.0, \\
299                 \> dt\_dopr = 3600.0, data\_output\_pr = 'u', \\
300                 \> ....... / \\ \end{tabbing}};
301   \end{tikzpicture}}
302   \normalsize
303\end{frame}
304
305% Folie 14
306\begin{frame}
307   \frametitle{How to set up turbulence recycling with PALM (II)}
308   \small
309   \begin{itemize}
310      \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
311            the file connection statement for restart data.}           
312   \end{itemize}
313   \begin{center}
314   \includegraphics[width=0.8\textwidth]{non_cyclic_figures/list_of_input_files.png}
315   \end{center} 
316   \begin{itemize}
317      \item<2->{The mrun-command to start the main run then has to look like \par\bigskip
318          {\tt mrun ... -r \dq d3\# turrec\dq}   \par\bigskip
319          The main run is allowed to use a different number of processors and a different domain decomposition than the precursor run!}
320   \end{itemize}
321\end{frame}
322
323\begin{frame}
324   \frametitle{How to set up turbulence recycling with PALM (III)}
325   \begin{itemize}
326      \item{\textbf{required} / recommended parameter settings for the main run:}
327   \end{itemize}
328   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\footnotesize]
329   \tikzstyle{box2} = [rectangle, draw, text width=0.4\textwidth, font=\tiny]
330   \tikzstyle{line} = [draw, -latex']
331   \begin{tikzpicture}     
332      \node[box](inipar){ \begin{tabbing} 
333         \&inipar \= ....... \\
334                  \\
335                  \> \textbf{turbulent\_inflow = .TRUE.}, \\ 
336                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, \\
337                  \> \textbf{psolver = 'multigrid'}, \\
338                  \> \textbf{initializing\_actions = 'cyclic\_fill'}, \\
339                  \> \textbf{recycling\_width = ...}, \\
340                  \> inflow\_damping\_height = ..., \\
341                  \> conserve\_volume\_flow = .T., \\
342                  \\
343                  \> ...... / \\ \end{tabbing}};
344      \uncover<2->{\node[box2] (horizontal_width) at (3,-0.6) {\textbf{Horizontal width of the recycling domain.}};}
345      \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,
346                                                information is automatically taken from the precursor data.}};}
347
348      \path<2->[line] (horizontal_width.west) -- (-1.2,-0.4);
349      \path<3->[line] (vertical_extend.west)  -- (-0.4,-0.9);
350   \end{tikzpicture}
351\end{frame}
352
353% Folie 16
354\begin{frame}
355   \frametitle{Final remarks}
356   \begin{itemize}
357      \item<1->{Non-cyclic boundary conditions and turbulence recycling method require extreme care with setting of the respective parameters.}
358      \item<2->{So far, these methods have been applied only to a few special cases (cold air outbreaks). Other setups may require modifications.}
359      \item<3->{Biggest problems are caused by gravity waves in capping inversions. Simulations with pure neutral stratification are expected to cause less problems.}
360   \end{itemize}
361\end{frame}
362
363\end{document}
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