source: palm/trunk/TUTORIAL/SOURCE/non_cyclic_boundary_conditions.tex @ 1387

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several updates in the tutorial

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1% $Id: non_cyclic_boundary_conditions.tex 1226 2013-09-18 13:19:19Z boeske $
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         \par\smallskip
69         \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.}
70         \par\smallskip
71         \item<6->{At the outflow, a boundary condition is required which allows the eddies to freely leave the domain.}
72      \end{itemize}
73   \end{itemize}   
74\end{frame}
75
76\section{Motivation}
77\subsection{Motivation}
78
79%Folie 3
80\begin{frame}
81   \frametitle{Motivation for Non-Cyclic Boundary Conditions}
82   \footnotesize
83   The main motivation for non-cyclic boundary conditions are studies of isolated phenomena.
84   \begin{tabbing}
85   \uncover<2->{\textbf{Example:} \= Turbulence generated by a single obstacle. \\}   
86                    \\
87                    \uncover<6->{ \> Cyclic boundary conditions along x would allow the generated turbulence\\
88                     \>  to enter the domain again, and so finally to modify the turbulence \\
89                     \>  on the leeward side of the building. \\ }     
90                     \\ 
91                     \uncover<9>{ \> This wouldn't be a simulation of a single building, but of an\\
92                     \> infinite row of buildings!   }
93   \end{tabbing}
94   \begin{center}
95   \includegraphics<3|handout:0>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_1.png}
96   \includegraphics<4|handout:0>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_2.png}
97   \includegraphics<5-6|handout:0>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_3.png}
98   \includegraphics<7|handout:0>[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_4.png}
99   \uncover<8-|handout:1>{\begin{center} \includegraphics[width=0.7\textwidth]{non_cyclic_figures/motivation_non_cyclic_5.png} \end{center}}
100   \end{center}
101   \normalsize
102\end{frame}
103
104% Folie 4
105\begin{frame}
106   \frametitle{Implications of Non-Cyclic Boundary Conditions}
107   \footnotesize
108   \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!}
109   \par\bigskip
110   \includegraphics<3|handout:0>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_1.png}
111   \includegraphics<4|handout:0>[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_2.png}
112   \uncover<5-|handout:1>{\includegraphics[width=0.8\textwidth]{non_cyclic_figures/implications_non_cyclic_3.png}}
113   \par\bigskip
114   \onslide<6->{Flow internal turbulence may develop, but this may require a very long model domain.}
115   \par\bigskip
116   \includegraphics<7|handout:0>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_4.png}
117   \includegraphics<8|handout:0>[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_5.png}
118   \uncover<9-|handout:1>{\includegraphics[width=\textwidth]{non_cyclic_figures/implications_non_cyclic_6.png}}
119   \onslide<10->{There is a need to supply turbulence information at the inflow.}
120\end{frame}
121
122\section{How to Create a Turbulent Inflow}
123\subsection{How to Create a Turbulent Inflow}
124
125% Folie 5
126\begin{frame}
127   \frametitle{How to Create a Turbulent Inflow (I)}
128   Two methods:
129   \begin{itemize}
130      \item<2->{by a statistical model}
131      \item<3->{by recycling-method  (Lund et al., 1998)}
132   \end{itemize}
133   \includegraphics<4|handout:0>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_1_neu.png}
134   \includegraphics<5|handout:0>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_2_neu.png}
135   \includegraphics<6|handout:0>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_3_neu.png}
136   \includegraphics<7|handout:0>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_4_neu.png}
137   \includegraphics<8|handout:0>[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_5_neu.png}
138   \uncover<9-|handout:1>{\includegraphics[width=\textwidth]{non_cyclic_figures/create_turbulent_inflow_1/create_turbulent_inflow_6.png}}
139   \par\bigskip
140   \uncover<10>{How do we get the initial turbulence in the recycle area? \\
141   If there is no turbulence, there is nothing to recycle!}
142\end{frame}
143
144%Folie 6
145\begin{frame}
146   \frametitle{How to Create a Turbulent Inflow (II)}
147   \footnotesize
148   Initial  turbulence is created by a precursor run with cyclic boundary conditions and much smaller domain size than used for the main run.
149   \tikzstyle{line} = [draw, blue, thick, dashed, -latex']   
150   \begin{tikzpicture}     
151      \uncover<1>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_1.png}};}
152      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_2.png}};}
153      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_2/create_turbulent_inflow_3.png}};}
154      \node(text) [right=0.1cm of picture]{
155         \parbox{5cm}{
156         \scriptsize
157         \begin{itemize}
158         \item<4->{When the precursor run is finished, data of the last timestep are stored on disc.}
159         \item<5->{These data are then read by the main run and repeatedly mapped to the main run domain, until it is completely filled.}
160         \end{itemize}}};
161     \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}};}
162     \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}};}
163     \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}};}
164     \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}};} 
165     \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}};} 
166     \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}};} 
167    \path<7->[line] (-0.45,-1) -- (-0.7,-2.6);
168    \path<7->[line] (1.78,-1) -- (1.68,-2.6); 
169    \path<8->[line] (-0.45,-1) -- (1.68,-2.6);
170    \path<8->[line] (1.78,-1) -- (4,-2.6);
171    \path<9->[line] (-0.45,-1) -- (4,-2.6);
172    \path<9->[line] (1.78,-1) -- (6.4,-2.6);
173    \path<10->[line] (-0.45,-1) -- (6.4,-2.6);
174    \path<10->[line] (1.78,-1) -- (6.9,-2.6);
175   \end{tikzpicture} 
176\end{frame}
177
178% Folie 7
179\begin{frame}
180   \frametitle{How to Create a Turbulent Inflow (III)}
181   \footnotesize
182   \begin{itemize}
183      \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
184            the last time step of the precursor run.}
185   \end{itemize}
186   \tikzstyle{line1} = [draw, red, thick, -latex']
187   \tikzstyle{line2} = [draw, red, thick, -]
188   \begin{tikzpicture}
189      \uncover<2>{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_1.png}};}
190      \uncover<3->{\node(picture) {\includegraphics[width=0.4\textwidth]{non_cyclic_figures/create_turbulent_inflow_3/create_turbulent_inflow_2.png}};}
191      \node(text) [right=0.1cm of picture]{
192         \parbox{6.5cm}{
193         \scriptsize
194         \begin{itemize}
195         \item<6->{Since the height of the turbulent boundary layer may increase with increasing distance from the inflow boundary, recycling has
196               to be limited to the height of the turbulent boundary layer at the inflow. Otherwise, the boundary layer height will continuously increase with time.}
197         \end{itemize}}};
198   \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}};}
199   \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}};}
200   \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}};}
201   \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}};}
202   \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}};}
203     
204   \path<5->[line2] (picture.east) -- (2.25,-1.3);
205   \path<5->[line2] (2.25,-1.3)    -- (-1.2,-1.3);
206   \path<5->[line2] (-1.2,-1.3)    -- (-1.2,-3.2);
207   \path<5->[line1] (-1.2,-3.2)      -- (-0.8,-3.2);
208   \end{tikzpicture}
209\end{frame}
210
211\section{Implementation in PALM}
212\subsection{Implementation in PALM}
213
214% Folie 8
215\begin{frame}
216   \frametitle{Non-Cyclic Boundary Conditions in PALM (I)}
217   \textbf{Status of availability:}
218   \begin{itemize}
219      \item<2->{Non-cyclic boundary conditions along \textbf{one} of the horizontal directions (\textit{x} \textbf{or} \textit{y}).}
220      \begin{itemize}
221         \item<3->{Dirichlet conditions at inflow (stationary vertical profiles, \textit{u}(\textit{z}), \textit{v}(\textit{z}),
222                   \textit{pt}(\textit{z}), \textit{q}(\textit{z}), \textit{w}=0).}
223         \item<4->{Radiation conditions at outflow. Tendencies at the boundary are replaced by e.g.}
224      \end{itemize}     
225      \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} 
226                     \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}}
227      \par\bigskip
228      \item<5->{Turbulence recycling method for inflow \textbf{from left}.}
229   \end{itemize} 
230\end{frame}
231
232% Folie 9
233\begin{frame}
234   \frametitle{Non-Cyclic Boundary Conditions in PALM (II)}
235   \par\bigskip
236   \small
237   \textbf{Further requirements for PALM runs using non-cyclic boundary conditions:}
238   \par\bigskip
239   \begin{itemize}
240      \item<2->{The \textbf{multigrid-method} has to be used for solving the Poisson-equation.}
241      \item<3->{A \textbf{damping zone} has sometimes to be activated in the vicinity of the in- and outflow in order to avoid reflection of gravity waves.}
242      \item<4->{\textbf{Volume flow conservation} should be activated, because otherwise flow acceleration or deceleration may occur along the non-cyclic direction.}
243      \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
244                inflow throughout the whole run, in order to maintain a turbulent state of the flow.}
245   \end{itemize}
246   \normalsize
247\end{frame}
248
249\section{Current Applications}
250\subsection{Current Applications}
251
252
253% Folie 10
254\begin{frame}
255   \frametitle{Current Applications of Non-Cyclic BCs (I)}
256   \textbf{Cold air outbreaks}
257   \par\bigskip
258   \includegraphics[width=\textwidth]{non_cyclic_figures/cold_air_outbreaks.png} \\
259   \par\bigskip
260   \tiny
261   \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.,
262   \textbf{35}, L23804, doi:10.1029/2008GL035845. \\
263   \par\bigskip
264   \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,
265    doi:10.1029/2005GL022872. \\
266   \normalsize
267   \begin{center} \uncover<2->{\textbf{Turbulence recycling has not been used!}} \end{center}
268\end{frame}
269
270% Folie 11
271\begin{frame}
272   \frametitle{Current Applications of Non-Cyclic BCs (II)}
273   \textbf{Cold air outbreaks}
274   \begin{center} 
275   \includegraphics[width=0.85\textwidth]{non_cyclic_figures/cold_air_outbreaks_2.png} \\
276   liquid water content (vertically intgrated) 
277   \end{center}
278\end{frame}
279
280\section{How to set up}
281\subsection{How to set up}
282
283% Folie 12
284\begin{frame}
285   \frametitle{How to set up non-cyclic runs with PALM}
286   \begin{itemize}
287      \item{\textbf{required} / recommended parameter settings:}
288   \end{itemize}
289   \par\bigskip
290   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
291   \begin{tikzpicture}     
292      \node[box](inipar){ \begin{tabbing} 
293         \&inipar \= ....... \\
294                  \\
295                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, (bc\_ns = 'dirichlet/radiation',) \\ 
296                  \> \textbf{psolver = 'multigrid'}, \\
297                  \\
298                  \> initializing\_actions = 'set\_1d-model\_profiles', \\
299                  \> conserve\_volume\_flow = .T., \\
300                  \\
301                  \> ...... / \\ \end{tabbing}};
302   \end{tikzpicture}
303\end{frame}
304
305% Folie 13
306\begin{frame}
307   \frametitle{How to set up turbulence recycling with PALM (I)}
308   \small
309   \begin{itemize}
310      \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.}
311      \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.
312                This enables writing of profiles to the restart file, which can then be used by the main run.}
313      \item<3->{Instead of using averaged profiles from the prerun, inflow profiles for the main run can also be prescribed using parameters u\_profile and v\_profile.}
314   \end{itemize}
315   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\small]
316   \onslide<2->{
317   \begin{tikzpicture}     
318      \node[box](inipar){ \begin{tabbing} 
319         \&d3par \= end\_time = 3600.0, \\
320                 \> dt\_dopr = 3600.0, data\_output\_pr = 'u', \\
321                 \> ....... / \\ \end{tabbing}};
322   \end{tikzpicture}}
323   \normalsize
324\end{frame}
325
326% Folie 14
327\begin{frame}
328   \frametitle{How to set up turbulence recycling with PALM (II)}
329   \small
330   \begin{itemize}
331      \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
332            the file connection statement for restart data.}           
333   \end{itemize}
334   \begin{center}
335   \includegraphics[width=0.8\textwidth]{non_cyclic_figures/list_of_input_files.png}
336   \end{center} 
337   \begin{itemize}
338      \item<2->{The mrun-command to start the main run then has to look like \par\bigskip
339          {\tt mrun ... -r \dq d3\# turrec\dq}   \par\bigskip
340          The main run is allowed to use a different number of processors and a different domain decomposition than the precursor run!}
341   \end{itemize}
342\end{frame}
343
344\begin{frame}
345   \frametitle{How to set up turbulence recycling with PALM (III)}
346   \begin{itemize}
347      \item{\textbf{required} / recommended parameter settings for the main run:}
348   \end{itemize}
349   \tikzstyle{box} = [rectangle, draw, text width=\textwidth, font=\footnotesize]
350   \tikzstyle{box2} = [rectangle, draw, text width=0.4\textwidth, font=\tiny]
351   \tikzstyle{line} = [draw, -latex']
352   \begin{tikzpicture}     
353      \node[box](inipar){ \begin{tabbing} 
354         \&inipar \= ....... \\
355                  \\
356                  \> \textbf{turbulent\_inflow = .TRUE.}, \\ 
357                  \> \textbf{bc\_lr = 'dirichlet/radiation'}, \\
358                  \> \textbf{psolver = 'multigrid'}, \\
359                  \> \textbf{initializing\_actions = 'cyclic\_fill'}, \\
360                  \> \textbf{recycling\_width = ...}, \\
361                  \> inflow\_damping\_height = ..., \\
362                  \> conserve\_volume\_flow = .T., \\
363                  \\
364                  \> ...... / \\ \end{tabbing}};
365      \uncover<2->{\node[box2] (horizontal_width) at (3,-0.6) {\textbf{Horizontal width of the recycling domain.}};}
366      \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,
367                                                information is automatically taken from the precursor data.}};}
368
369      \path<2->[line] (horizontal_width.west) -- (-1.2,-0.4);
370      \path<3->[line] (vertical_extend.west)  -- (-0.4,-0.9);
371   \end{tikzpicture}
372\end{frame}
373
374\section{Final remarks}
375\subsection{Final remarks}
376
377% Folie 16
378\begin{frame}
379   \frametitle{Final remarks}
380   \begin{itemize}
381      \item<1->{Non-cyclic boundary conditions and turbulence recycling method require extreme care with setting of the respective parameters.}
382      \item<2->{So far, these methods have been applied only to a few special cases (cold air outbreaks, urban canopy layer for neutral stratification). Other setups may require modifications.}
383      \item<3->{Biggest problems are caused by gravity waves in capping inversions. Simulations with pure neutral stratification cause less problems.}
384   \end{itemize}
385\end{frame}
386
387\end{document}
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