source: palm/trunk/TUTORIAL/SOURCE/non_cyclic_boundary_conditions.tex @ 964

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1% $Id: non_cyclic_boundary_conditions.tex 945 2012-07-17 15:43:01Z raasch $
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\section{Motivation}
75\subsection{Motivation}
76
77%Folie 3
78\begin{frame}
79   \frametitle{Motivation for Non-Cyclic Boundary Conditions}
80   \footnotesize
81   The main motivation for non-cyclic boundary conditions are studies of isolated phenomena.
82   \begin{tabbing}
83   \uncover<2->{\textbf{Example:} \= Turbulence generated by a single obstacle. \\}                   
84                    \uncover<6->{ \> Cyclic boundary conditions along x would allow the generated turbulence\\
85                     \>  to enter the domain again, and so finally to modify the turbulence \\
86                     \>  on the leeward side of the building. \\ }     
87                     \\ 
88                     \uncover<9>{ \> This wouldn't be a simulation of a single building, but of an\\
89                     \> infinite row of buildings! \\  }
90   \end{tabbing}
91   \begin{center}
92   \includegraphics<3>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_1.png}
93   \includegraphics<4>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_2.png}
94   \includegraphics<5-6>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_3.png}
95   \includegraphics<7>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_4.png}
96   \uncover<8->{\begin{center} \includegraphics[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_5.png} \end{center}}
97   \end{center}
98   \normalsize
99\end{frame}
100
101% Folie 4
102\begin{frame}
103   \frametitle{Implications of Non-Cyclic Boundary Conditions}
104   \footnotesize
105   \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!}
106   \par\bigskip
107   \includegraphics<3>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_1.png}
108   \includegraphics<4>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_2.png}
109   \uncover<5->{\includegraphics[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_3.png}}
110   \par\bigskip
111   \onslide<6->{Flow internal turbulence may develop, but this may require a very long model domain.}
112   \par\bigskip
113   \includegraphics<7>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_4.png}
114   \includegraphics<8>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_5.png}
115   \uncover<9->{\includegraphics[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_6.png}}
116   \onslide<10->{There is a need to supply turbulence information at the inflow.}
117\end{frame}
118
119\section{How to Create a Turbulent Inflow}
120\subsection{How to Create a Turbulent Inflow}
121
122% Folie 5
123\begin{frame}
124   \frametitle{How to Create a Turbulent Inflow (I)}
125   Two methods:
126   \begin{itemize}
127      \item<2->{by a statistical model}
128      \item<3->{by recycling-method  (Lund et al., 1998)}
129   \end{itemize}
130   \includegraphics<4>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_1_neu.png}
131   \includegraphics<5>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_2_neu.png}
132   \includegraphics<6>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_3_neu.png}
133   \includegraphics<7>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_4_neu.png}
134   \includegraphics<8>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_5_neu.png}
135   \uncover<9->{\includegraphics[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_6.png}}
136   \par\bigskip
137   \uncover<10>{How do we get the initial turbulence in the recycle area? \\
138   If there is no turbulence, there is nothing to recycle!}
139\end{frame}
140
141%Folie 6
142\begin{frame}
143   \frametitle{How to Create a Turbulent Inflow (II)}
144   \footnotesize
145   Initial  turbulence is created by a precursor run with cyclic boundary conditions and much smaller domain size than used for the main run.
146   \tikzstyle{line} = [draw, blue, thick, dashed, -latex']   
147   \begin{tikzpicture}     
148      \uncover<1>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_1.png}};}
149      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_2.png}};}
150      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_3.png}};}
151      \node(text) [right=0.1cm of picture]{
152         \parbox{5cm}{
153         \scriptsize
154         \begin{itemize}
155         \item<4->{When the precursor run is finished, data of the last timestep are stored on disc.}
156         \item<5->{These data are then read by the main run and repeatedly mapped to the main run domain, until it is completely filled.}
157         \end{itemize}}};
158     \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}};}
159     \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}};}
160     \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}};}
161     \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}};} 
162     \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}};} 
163     \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}};} 
164    \path<7->[line] (-0.45,-1) -- (-0.7,-2.6);
165    \path<7->[line] (1.78,-1) -- (1.68,-2.6); 
166    \path<8->[line] (-0.45,-1) -- (1.68,-2.6);
167    \path<8->[line] (1.78,-1) -- (4,-2.6);
168    \path<9->[line] (-0.45,-1) -- (4,-2.6);
169    \path<9->[line] (1.78,-1) -- (6.4,-2.6);
170    \path<10->[line] (-0.45,-1) -- (6.4,-2.6);
171    \path<10->[line] (1.78,-1) -- (6.9,-2.6);
172   \end{tikzpicture} 
173\end{frame}
174
175% Folie 7
176\begin{frame}
177   \frametitle{How to Create a Turbulent Inflow (III)}
178   \footnotesize
179   \begin{itemize}
180      \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
181            the last time step of the precursor run.}
182   \end{itemize}
183   \tikzstyle{line1} = [draw, red, thick, -latex']
184   \tikzstyle{line2} = [draw, red, thick, -]
185   \begin{tikzpicture}
186      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_1.png}};}
187      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_2.png}};}
188      \node(text) [right=0.1cm of picture]{
189         \parbox{6.5cm}{
190         \scriptsize
191         \begin{itemize}
192         \item<6->{Since the height of the turbulent boundary layer may increase with increasing distance from the inflow boundary, recycling has
193               to be limited to the height of the turbulent boundary layer at the inflow. Otherwise, the boundary layer height will continuously increase with time.}
194         \end{itemize}}};
195   \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}};}
196   \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}};}
197   \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}};}
198   \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}};}
199   \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}};}
200     
201   \path<5->[line2] (picture.east) -- (2.25,-1.3);
202   \path<5->[line2] (2.25,-1.3)    -- (-1.2,-1.3);
203   \path<5->[line2] (-1.2,-1.3)    -- (-1.2,-3.2);
204   \path<5->[line1] (-1.2,-3.2)      -- (-0.8,-3.2);
205   \end{tikzpicture}
206\end{frame}
207
208\section{Implementation in PALM}
209\subsection{Implementation in PALM}
210
211% Folie 8
212\begin{frame}
213   \frametitle{Non-Cyclic Boundary Conditions in PALM (I)}
214   \textbf{Status of availability:}
215   \begin{itemize}
216      \item<2->{Non-cyclic boundary conditions along \textbf{one} of the horizontal directions (\textit{x} \textbf{or} \textit{y}).}
217      \begin{itemize}
218         \item<3->{Dirichlet conditions at inflow (stationary vertical profiles, \textit{u}(\textit{z}), \textit{v}(\textit{z}),
219                   \textit{pt}(\textit{z}), \textit{q}(\textit{z}), \textit{w}=0).}
220         \item<4->{Radiation conditions at outflow. Tendencies at the boundary are replaced by e.g.}
221      \end{itemize}     
222      \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} 
223                     \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}}
224      \par\bigskip
225      \item<5->{Turbulence recycling method for inflow \textbf{from left}.}
226   \end{itemize} 
227\end{frame}
228
229% Folie 9
230\begin{frame}
231   \frametitle{Non-Cyclic Boundary Conditions in PALM (II)}
232   \par\bigskip
233   \small
234   \textbf{Further requirements for PALM runs using non-cyclic boundary conditions:}
235   \par\bigskip
236   \begin{itemize}
237      \item<2->{The \textbf{multigrid-method} has to be used for solving the Poisson-equation.}
238      \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.}
239      \item<4->{\textbf{Volume flow conservation} should be activated, because otherwise flow acceleration or deceleration may occur along the non-cyclic direction.}
240      \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
241                inflow throughout the whole run, in order to maintain a turbulent state of the flow.}
242   \end{itemize}
243   \normalsize
244\end{frame}
245
246\section{Current Applications}
247\subsection{Current Applications}
248
249
250% Folie 10
251\begin{frame}
252   \frametitle{Current Applications of Non-Cyclic BCs (I)}
253   \textbf{Cold air outbreaks}
254   \par\bigskip
255   \includegraphics[width=\textwidth]{non_cyclic_figures/cold_air_outbreaks.png} \\
256   \par\bigskip
257   \tiny
258   \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.,
259   \textbf{35}, L23804, doi:10.1029/2008GL035845. \\
260   \par\bigskip
261   \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,
262    doi:10.1029/2005GL022872. \\
263   \normalsize
264   \begin{center} \uncover<2->{\textbf{Turbulence recycling has not been used!}} \end{center}
265\end{frame}
266
267% Folie 11
268\begin{frame}
269   \frametitle{Current Applications of Non-Cyclic BCs (II)}
270   \textbf{Cold air outbreaks}
271   \begin{center} 
272   \includegraphics[width=0.85\textwidth]{non_cyclic_figures/cold_air_outbreaks_2.png} \\
273   liquid water content (vertically intgrated) 
274   \end{center}
275\end{frame}
276
277\section{How to set up}
278\subsection{How to set up}
279
280% Folie 12
281\begin{frame}
282   \frametitle{How to set up non-cyclic runs with PALM}
283   \begin{itemize}
284      \item{\textbf{required} / recommended parameter settings:}
285   \end{itemize}
286   \par\bigskip
287   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
288   \begin{tikzpicture}     
289      \node[box](inipar){ \begin{tabbing} 
290         \&inipar \= ....... \\
291                  \\
292                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, (bc\_ns = 'dirichlet/radiation',) \\ 
293                  \> \textbf{psolver = 'multigrid'}, \\
294                  \\
295                  \> initializing\_actions = 'set\_1d-model\_profiles', \\
296                  \> conserve\_volume\_flow = .T., \\
297                  \\
298                  \> ...... / \\ \end{tabbing}};
299   \end{tikzpicture}
300\end{frame}
301
302% Folie 13
303\begin{frame}
304   \frametitle{How to set up turbulence recycling with PALM (I)}
305   \small
306   \begin{itemize}
307      \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.}
308      \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.
309                This enables writing of profiles to the restart file, which can then be used by the main run.}
310   \end{itemize}
311   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
312   \onslide<2->{
313   \begin{tikzpicture}     
314      \node[box](inipar){ \begin{tabbing} 
315         \&d3par \= end\_time = 3600.0, \\
316                 \> dt\_dopr = 3600.0, data\_output\_pr = 'u', \\
317                 \> ....... / \\ \end{tabbing}};
318   \end{tikzpicture}}
319   \normalsize
320\end{frame}
321
322% Folie 14
323\begin{frame}
324   \frametitle{How to set up turbulence recycling with PALM (II)}
325   \small
326   \begin{itemize}
327      \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
328            the file connection statement for restart data.}           
329   \end{itemize}
330   \begin{center}
331   \includegraphics[width=0.8\textwidth]{non_cyclic_figures/list_of_input_files.png}
332   \end{center} 
333   \begin{itemize}
334      \item<2->{The mrun-command to start the main run then has to look like \par\bigskip
335          {\tt mrun ... -r \dq d3\# turrec\dq}   \par\bigskip
336          The main run is allowed to use a different number of processors and a different domain decomposition than the precursor run!}
337   \end{itemize}
338\end{frame}
339
340\begin{frame}
341   \frametitle{How to set up turbulence recycling with PALM (III)}
342   \begin{itemize}
343      \item{\textbf{required} / recommended parameter settings for the main run:}
344   \end{itemize}
345   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\footnotesize]
346   \tikzstyle{box2} = [rectangle, draw, text width=0.4\textwidth, font=\tiny]
347   \tikzstyle{line} = [draw, -latex']
348   \begin{tikzpicture}     
349      \node[box](inipar){ \begin{tabbing} 
350         \&inipar \= ....... \\
351                  \\
352                  \> \textbf{turbulent\_inflow = .TRUE.}, \\ 
353                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, \\
354                  \> \textbf{psolver = 'multigrid'}, \\
355                  \> \textbf{initializing\_actions = 'cyclic\_fill'}, \\
356                  \> \textbf{recycling\_width = ...}, \\
357                  \> inflow\_damping\_height = ..., \\
358                  \> conserve\_volume\_flow = .T., \\
359                  \\
360                  \> ...... / \\ \end{tabbing}};
361      \uncover<2->{\node[box2] (horizontal_width) at (3,-0.6) {\textbf{Horizontal width of the recycling domain.}};}
362      \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,
363                                                information is automatically taken from the precursor data.}};}
364
365      \path<2->[line] (horizontal_width.west) -- (-1.2,-0.4);
366      \path<3->[line] (vertical_extend.west)  -- (-0.4,-0.9);
367   \end{tikzpicture}
368\end{frame}
369
370\section{Final remarks}
371\subsection{Final remarks}
372
373% Folie 16
374\begin{frame}
375   \frametitle{Final remarks}
376   \begin{itemize}
377      \item<1->{Non-cyclic boundary conditions and turbulence recycling method require extreme care with setting of the respective parameters.}
378      \item<2->{So far, these methods have been applied only to a few special cases (cold air outbreaks). Other setups may require modifications.}
379      \item<3->{Biggest problems are caused by gravity waves in capping inversions. Simulations with pure neutral stratification are expected to cause less problems.}
380   \end{itemize}
381\end{frame}
382
383\end{document}
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