source: palm/trunk/TUTORIAL/SOURCE/particle_model.tex @ 945

Last change on this file since 945 was 945, checked in by maronga, 12 years ago

added/updated several tutorial files

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1% $Id: particle_model.tex 945 2012-07-17 15:43:01Z 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\usetikzlibrary{calc}                             %neues paket
18\usetikzlibrary{decorations.markings}             %neues paket
19\usetikzlibrary{decorations.pathreplacing}        %neues paket
20\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
21\usepackage{amsmath}
22\usepackage{amssymb}
23\usepackage{multicol}
24\usepackage{pdfcomment}
25\usepackage{graphicx}
26\usepackage{listings}
27\lstset{showspaces=false,language=fortran,basicstyle=
28        \ttfamily,showstringspaces=false,captionpos=b}
29
30\institute{Institut fÌr Meteorologie und Klimatologie, Leibniz UniversitÀt Hannover}
31\date{last update: \today}
32\event{PALM Seminar}
33\setbeamertemplate{navigation symbols}{}
34
35\setbeamertemplate{footline}
36  {
37    \begin{beamercolorbox}[rightskip=-0.1cm]&
38     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
39    \end{beamercolorbox}
40    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,
41      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}
42      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}
43    \end{beamercolorbox}
44    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}
45    \end{beamercolorbox}
46  }
47%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}}
48
49\title[PALM's Lagrangian Particle Model]{PALM's Lagrangian Particle Model}
50\author{Siegfried Raasch}
51
52\begin{document}
53
54% Folie 1
55\begin{frame}
56\titlepage
57\end{frame}
58
59\section{The embedded Lagrangian particle model}
60\subsection{The embedded Lagrangian particle model}
61
62% Folie 2
63\begin{frame}
64   \frametitle{Overview}
65
66   \begin{itemize}     
67           \item<1-> The Lagrangian particle model embedded in PALM can be used for
68different purposes:
69           \begin{itemize}
70           \footnotesize
71              \item Cloud droplet simulation
72              \item Dispersion modelling / Footprint analysis
73              \item Visualization
74      \end{itemize}   
75      \vspace{3mm}
76      \item<2-> Therefore the particles can have different properties, e.g.:
77      \begin{itemize}
78         \footnotesize
79              \item Particles can be transported (advected) \textbf{passively} with the \textbf{resolved-scale} flow
80              \item Particle transport by the subgrid-scale (SGS) turbulence can be included by switching on a stochastic SGS model for the particle transport (parameter: \texttt{use\underline{ }sgs\underline{ }for\underline{ }particles})
81              \item Particles can be given a mass and thus an \textbf{inertia} and a \textbf{radius} which affects their \textbf{flow resistance} (parameter: \texttt{density\underline{ }ratio}, \texttt{radius})
82              \item Tails can be added to the particles (showing the particle trajectories) for visualization purpose using the special visualization package \textbf{dvrp}
83      \end{itemize}   
84   \end{itemize}   
85\end{frame}
86
87
88% Folie 3
89\begin{frame}
90   \frametitle{Basics (I)}
91
92   \begin{itemize}     
93           \item<1-> The particle model is switched on by adding a \texttt{\&particles\underline{ }par} NAMELIST to the parameter file (PARIN). This NAMELIST has to be added \textbf{after} the \texttt{\&d3par}-NAMELIST.
94           \item All parameters for steering the particle model are described in: Documentation $\rightarrow$ Model steering $\rightarrow$ Parameters $\rightarrow$ Particles (http://palm.muk.uni-hannover.de/)
95           \item \textbf{The particle model requires to use a constant vertical grid spacing (due to the implemented scheme for the interpolation of information from the LES grid to particle positions, that is required for the calculation of particle velocities)!}
96   \end{itemize}
97\end{frame}
98
99% Folie 4
100\begin{frame}
101   \frametitle{Basic Particle Parameters (I)}
102   \small
103   Parameters that define the locations of particle source(s):
104   \begin{itemize}
105      \item Step I: Define the volume of the particle source
106   \end{itemize}
107
108   \begin{tikzpicture}
109      \definecolor{darkgreen1}{rgb}{0.2,0.7,0.2}
110      \definecolor{darkgreen2}{rgb}{0.4,0.7,0.4}
111      \definecolor{darkgreen3}{rgb}{0.1,0.6,0.2}
112     
113      % Draw the box
114      \onslide<2->
115      \draw[-] (0,0) -- (5,0);
116      \draw[-] (0,0) -- (0,4);
117      \draw[-] (5,4) -- (5,0);
118      \draw[-] (0,4) -- (5,4);
119      \draw[-] (2,1.5) -- (7,1.5);
120      \draw[-] (2,1.5) -- (2,5.5);
121      \draw[-] (7,5.5) -- (7,1.5);
122      \draw[-] (2,5.5) -- (7,5.5);
123      \draw[-] (0,0) -- (2,1.5);
124      \draw[-] (5,0) -- (7,1.5);
125      \draw[-] (5,4) -- (7,5.5);
126      \draw[-] (0,4) -- (2,5.5);
127      \node at (4,5) {\small Total model domain};
128     
129      % Draw coordinate system
130      \node at (8.5,2.5) [scale=1.0] {%
131      \begin{tikzpicture}
132         \draw[->] (0,0) -- (1,0);
133         \draw[->] (0,0) -- (0,1);
134         \draw[->] (0,0) -- (0.5,0.5);
135         \node at (-0.2,0.9) {z};
136         \node at (0.9,-0.2) {x};
137         \node at (0.65,0.3) {y};
138      \end{tikzpicture}
139      };
140     
141      % Draw green box
142      \onslide<3->
143      \draw[fill=darkgreen1,draw=darkgreen1,opacity=.95]
144         (0,1) --
145         (3,1) --
146         (3,2.5) --
147         (0,2.5) -- cycle ;
148      \draw[fill=darkgreen2,draw=darkgreen2,opacity=.95]
149         (3,1) --
150         (4,1.75) --
151         (4,3.25) --
152         (3,2.5) -- cycle ;
153      \draw[fill=darkgreen3,draw=darkgreen3,opacity=.95]
154         (0,2.5) --
155         (3,2.5) --
156         (4,3.25) --
157         (1,3.25) -- cycle ;
158      \node at (1.5,2) {\small \glqq Source Volume\grqq };         
159     
160      % Dashed green lines   
161      \draw[dashed, ultra thick, color=darkgreen3] (0,1) -- (0,0);
162      \draw[dashed, ultra thick, color=darkgreen3] (3,1) -- (3,0);
163      \draw[dashed, ultra thick, color=darkgreen3] (3,1) -- (5,1);
164      \draw[dashed, ultra thick, color=darkgreen3] (4,1.75) -- (6,1.75);
165      \draw[dashed, ultra thick, color=darkgreen3] (5,1) -- (5,0);
166      \draw[dashed, ultra thick, color=darkgreen3] (6,1.75) -- (6,0.75);
167     
168      % Add Labels
169      \node at (1,-0.25) {\scriptsize \texttt{ps1} (default 0.0)};
170      \node at (4.25,-0.25) {\scriptsize \texttt{psr} (default \texttt{nx*dx})};
171      \node at (7,0) {\scriptsize \texttt{pss} (default 0.0)};
172      \node at (8,0.75) {\scriptsize \texttt{psn} (default \texttt{ny*dy})};
173      \node [text width=4em] at (-0.7,0.5) {\scriptsize \texttt{psb} (default zu(\texttt{nz}/2))};
174      \node [text width=4em] at (-0.7,2) {\scriptsize \texttt{pst} (default zu(\texttt{nz}/2))}
175     
176   \onslide<1->
177   \end{tikzpicture}
178\end{frame}
179
180% Folie 5
181\begin{frame}
182   \frametitle{Basic Particle Parameters (II)}
183   \small
184   Parameters that define the locations of particle source(s):
185   \begin{itemize}
186      \item Step IIa: Define the points of single particle release   
187   \end{itemize}
188   
189   \begin{tikzpicture}
190      \definecolor{darkgreen}{rgb}{0.0,0.35,0.0}
191      \definecolor{darkgreen3}{rgb}{0.2,0.6,0.2}
192      \definecolor{darkred}{rgb}{0.5,0.0,0.0}
193     
194      % Draw green box (except for one line that is drawn later)
195      \draw[-, ultra thick, color=darkgreen3] (0,0) -- (5,0);
196      \draw[-, ultra thick, color=darkgreen3] (0,0) -- (0,4);
197      \draw[-, ultra thick, color=darkgreen3] (0,4) -- (5,4);
198      \draw[-, ultra thick, color=darkgreen3] (2,1.5) -- (7,1.5);
199      \draw[-, ultra thick, color=darkgreen3] (2,1.5) -- (2,5.5);
200      \draw[-, ultra thick, color=darkgreen3] (7,5.5) -- (7,1.5);
201      \draw[-, ultra thick, color=darkgreen3] (2,5.5) -- (7,5.5);
202      \draw[-, ultra thick, color=darkgreen3] (0,0) -- (2,1.5);
203      \draw[-, ultra thick, color=darkgreen3] (5,0) -- (7,1.5);
204      \draw[-, ultra thick, color=darkgreen3] (5,4) -- (7,5.5);
205      \draw[-, ultra thick, color=darkgreen3] (0,4) -- (2,5.5);
206      \node at (4,5) {\small \glqq Source Volume\grqq};
207     
208      % Draw circles and dashed lines
209      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (0,0) {};
210      \node at (0,0) {1};
211      \onslide<2->
212      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (2,0) {};
213      \draw[dashed, ultra thick, color=blue] (rd1) -- (rd2);
214      \node at (2,0) {2};
215      \node at (1,-0.25) {\scriptsize \texttt{pdx}};
216      \onslide<3->
217      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (4,0) {};
218      \draw[dashed, ultra thick, color=blue] (rd2) -- (rd3);
219      \node at (4,0) {3};
220      \onslide<4>
221      \node[circle, draw, thick, fill=red!90, scale=1.1] (rdx1) at (6,0) {};
222      \draw[dashed, ultra thick, color=blue] (rd3) -- (rdx1);
223      \node[scale=1.6] at (6,0) {X};
224      \onslide<6->
225      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (1.5,1.125) {};
226      \draw[dashed, ultra thick, color=darkgreen] (rd1) -- (rd4);     
227      \node at (1.5,1.125) {4}
228      \node at (1.1,0.43) {\scriptsize \texttt{pdy}};
229      \onslide<7->
230      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (3.5,1.125) {};
231      \draw[dashed, ultra thick, color=blue] (rd4) -- (rd5);
232      \node at (3.5,1.125) {5};
233      \onslide<7->      
234      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (5.5,1.125) {};
235      \draw[dashed, ultra thick, color=blue] (rd5) -- (rd6);
236      \node at (5.5,1.125) {6};
237      \onslide<8>
238      \node[circle, draw, thick, fill=red!90, scale=1.1] (rdx2) at (3,2.25) {};   
239      \draw[dashed, ultra thick, color=darkgreen] (rd4) -- (rdx2);
240      \node[scale=1.6] at (3,2.25) {X};
241      \onslide<10->      
242      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (0,2.2) {};
243      \draw[dashed, ultra thick, color=darkred] (rd1) -- (rd7);
244      \node at (0,2.2) {7};
245      \node at (0.3,1.3) {\scriptsize \texttt{pdz}};
246      \onslide<11->
247      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (2,2.2) {};
248      \draw[dashed, ultra thick, color=blue] (rd7) -- (rd8);
249      \node at (2,2.2) {8};
250      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (4,2.2) {};
251      \draw[dashed, ultra thick, color=blue] (rd8) -- (rd9);
252      \node at (4,2.2) {9};
253      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (1.5,3.325) {};
254      \draw[dashed, ultra thick, color=darkgreen] (rd7) -- (rd10);     
255      \node[scale=0.8] at (1.5,3.325) {10}
256      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (3.5,3.325) {};
257      \draw[dashed, ultra thick, color=blue] (rd10) -- (rd11);
258      \node[scale=0.8] at (3.5,3.325) {11};
259      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (5.5,3.325) {};
260      \draw[dashed, ultra thick, color=blue] (rd11) -- (rd12);
261      \node[scale=0.8] at (5.5,3.325) {12};           
262      \onslide<12>      
263      \node[circle, draw, thick, fill=red!90, scale=1.1] (rdx3) at (0,4.4) {};
264      \draw[dashed, ultra thick, color=darkred] (rd7) -- (rdx3);
265      \node[scale=1.6] at (0,4.4) {X};
266     
267      % Draw rest of the green box
268      \onslide<1-13>
269      \draw[-, ultra thick, color=darkgreen3] (5,4) -- (5,0);
270     
271      % Draw coordinate system
272      \node at (7.2,0.1) [scale=1.0] {%
273      \begin{tikzpicture}
274         \draw[->] (0,0) -- (1,0);
275         \draw[->] (0,0) -- (0,1);
276         \draw[->] (0,0) -- (0.5,0.5);
277         \node at (-0.2,0.9) {z};
278         \node at (0.9,-0.2) {x};
279         \node at (0.65,0.3) {y};
280      \end{tikzpicture}
281      };
282     
283      % Add text
284      \node at (9.0,3) [scale=0.8] {%
285      \begin{tikzpicture}
286         \node[text width=11em] {\scriptsize \texttt{maximum\underline{ }number\underline{ }of\underline{ }particles} number of particles (per PE) for that memory must be allocated at the beginning of a run; this number must be $\ge$ the initial number of particles \textbf{per subdomain(!)}.\\ \ \\ \textbf{Attention:} If netCDF output of particle data is switched on, \texttt{maximum\underline{ }number\underline{ }of\underline{ }particles} must be $\ge$ the maximum number of particles per subdomain observed throughout the complete run!\\ \ \\ Choosing a too large value may cause memory problems!\\};
287      \end{tikzpicture}
288      };     
289     
290   \end{tikzpicture}
291   
292\end{frame}
293
294% Folie 6
295\begin{frame}
296   \frametitle{Basic Particle Parameters (III)}
297   \small
298   Parameters that define the locations of particle source(s):
299   \begin{itemize}
300      \item Step IIb: Random start positions of particles
301   \end{itemize}
302   
303   \begin{tikzpicture}
304      \definecolor{darkgreen3}{rgb}{0.2,0.6,0.2}
305
306      % Draw green box
307      \draw[-, ultra thick, color=darkgreen3] (0,0) -- (5,0);
308      \draw[-, ultra thick, color=darkgreen3] (0,0) -- (0,4);
309      \draw[-, ultra thick, color=darkgreen3] (5,4) -- (5,0);
310      \draw[-, ultra thick, color=darkgreen3] (0,4) -- (5,4);
311      \draw[-, ultra thick, color=darkgreen3] (2,1.5) -- (7,1.5);
312      \draw[-, ultra thick, color=darkgreen3] (2,1.5) -- (2,5.5);
313      \draw[-, ultra thick, color=darkgreen3] (7,5.5) -- (7,1.5);
314      \draw[-, ultra thick, color=darkgreen3] (2,5.5) -- (7,5.5);
315      \draw[-, ultra thick, color=darkgreen3] (0,0) -- (2,1.5);
316      \draw[-, ultra thick, color=darkgreen3] (5,0) -- (7,1.5);
317      \draw[-, ultra thick, color=darkgreen3] (5,4) -- (7,5.5);
318      \draw[-, ultra thick, color=darkgreen3] (0,4) -- (2,5.5);
319
320     
321      % Draw circles and dashed lines
322      \onslide<1-3>
323      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (4,0) {};
324      \node at (4,0) {3};
325      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (4,2.2) {};
326      \node at (4,2.2) {9};
327
328      \onslide<1>
329      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (0,0) {};
330      \node at (0,0) {1};
331      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (2,0) {};
332      \node at (2,0) {2};
333      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (1.5,1.125) {};
334      \node at (1.5,1.125) {4};
335      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (3.5,1.125) {};
336      \node at (3.5,1.125) {5};
337      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (5.5,1.125) {};
338      \node at (5.5,1.125) {6};
339      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (0,2.2) {};
340      \node at (0,2.2) {7};
341      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (2,2.2) {};
342      \node at (2,2.2) {8};
343      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (1.5,3.325) {};
344      \node[scale=0.8] at (1.5,3.325) {10}
345      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (3.5,3.325) {};
346      \node[scale=0.8] at (3.5,3.325) {11};
347      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (5.5,3.325) {};
348      \node[scale=0.8] at (5.5,3.325) {12};
349                 
350      \onslide<3>
351      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1n) at (1.0,0.3) {};
352      \node at (1.0,0.3) {1};
353      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2n) at (1.8,0.3) {};
354      \node at (1.8,0.3) {2};
355      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4n) at (1.7,1.0) {};
356      \node at (1.7,1.0) {4};
357      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5n) at (3.0,1.2) {};
358      \node at (3.0,1.2) {5};
359      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6n) at (4.5,1.125) {};
360      \node at (4.5,1.125) {6};
361      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7n) at (0.9,2.8) {};
362      \node at (0.9,2.8) {7};
363      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8n) at (3,1.8) {};
364      \node at (3,1.8) {8};
365      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10n) at (2.1,3) {};
366      \node[scale=0.8] at (2.1,3) {10};     
367      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11n) at (4,4.5) {};
368      \node[scale=0.8] at (4,4.5) {11};
369      \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12n) at (4.5,3.2) {};
370      \node[scale=0.8] at (4.5,3.2) {12};     
371     
372      % Draw coordinate system
373      \onslide<1->
374      \node at (9,2) [scale=1.0] {%
375      \begin{tikzpicture}
376         \draw[->] (0,0) -- (1,0);
377         \draw[->] (0,0) -- (0,1);
378         \draw[->] (0,0) -- (0.5,0.5);
379         \node at (-0.2,0.9) {z};
380         \node at (0.9,-0.2) {x};
381         \node at (0.65,0.3) {y};
382      \end{tikzpicture}
383      };
384     
385      % Add text
386      \node at (9.2,4) {\scriptsize \texttt{random\underline{ }start\underline{ }position = .T.}};
387     
388   \end{tikzpicture}
389   
390\end{frame}
391
392% Folie 7
393\begin{frame}
394   \frametitle{Basic Particle Parameters (IV)}
395   \small
396   Parameters that define the period of particle release: \\
397   \vspace{10mm}
398   \begin{columns}[T]
399      \begin{column}{1.15\textwidth}
400         \begin{tikzpicture}
401            \definecolor{darkred}{rgb}{0.6,0.1,0.1}
402            \definecolor{grey}{rgb}{0.25,0.25,0.25}
403            \draw[->, ultra thick] (0,0) -- (10.5,0);
404            \draw[->, ultra thick] (0,0.5) -- (0,-0.5);
405            \node at (10.7,0) {t};
406            \node at (0,-0.8) {0};   
407            \node[text width=6em] at (0.2,-1.9) {\scriptsize Start of LES, determination of particle release points};
408     
409            \onslide<2->
410            \draw[->, ultra thick, color=red] (2.5,0.5) -- (2.5,-0.5);
411            \node at (2.8,-0.8) {\scriptsize \texttt{particle\underline{ }advection\underline{ }start}};       
412            \node[text width=6em] at (2.8,-2.1) {\scriptsize Calculation of particle trajectories begins (default value: 0.0)};
413     
414     
415     
416     
417            \onslide<3->
418            \draw[->, ultra thick, color=red] (5,0.5) -- (5,-0.5);
419            \node[text width=4em] at (4.8,-1.7) {\scriptsize Release of a new set of particles}
420            \node at (3.75,0.3) {\scriptsize \texttt{dt\underline{ }prel}};
421            \draw[<->, thick, color=blue] (2.5,0.6) -- (4.95,0.6);
422     
423     
424     
425            \onslide<4->
426            \draw[->, ultra thick, color=darkred] (6.5,0.5) -- (6.5,-0.5);   
427            \node[text width=5em] at (6.7,-1.7) {\scriptsize Deletion of the first set of particles};
428            \draw[<->, thick, color=darkred] (2.5,0.9) -- (6.5,0.9);
429            \node at (4.5,1.2) {\scriptsize \texttt{particle\underline{ }maximum\underline{ }age}};
430     
431            \onslide<5->
432            \draw[->, ultra thick, color=darkred] (8.5,0.5) -- (8.5,-0.5); 
433            \node[text width=5em] at (8.6,-1.9) {\scriptsize No release of new particles after this time};
434            \node at (8.5,-0.8) {\scriptsize \texttt{end\underline{ }time\underline{ }prel}};
435            \draw[<->, thick, color=blue] (5.05,0.6) -- (8.5,0.6);
436
437            \onslide<6->
438            \draw[->, ultra thick, color=grey] (10.2,0.5) -- (10.2,-0.5);     
439            \node[text width=5em] at (10.7,-1.9) {\scriptsize Deletion of the second set of particles};
440            \draw[<->, thick, color=darkred] (5.0,1.6) -- (10.2,1.6);
441           
442            \onslide<1->
443         \end{tikzpicture}
444       \end{column}
445   \end{columns}
446
447 
448\end{frame}
449
450% Folie 8
451\begin{frame}[t]
452   \frametitle{Basic Particle Parameters (V)}
453   \small
454   Parameter that defines the mode of particle movement: \\
455   The concept of LES ...\\
456   \vspace{-5mm}
457   \begin{center}
458      \includegraphics[scale=0.1]{particle_model_figures/basic_particle_parameters_5.png}
459   \end{center}
460   \vspace{-5mm}
461   \onslide<2->
462   ... transferred to the embedded particle model leads to particle velocity\\
463   \vspace{1mm}
464   \begin{columns}[T]
465      \begin{column}{0.35\textwidth}
466         $\vec{V}_{i_{\text{particle}}} = \vec{V}_{i_{\text{resolved}}} + \vec{V}_{i_{\text{subgrid}}}$
467      \end{column}
468      \begin{column}{0.55\textwidth}
469         \scriptsize
470         \onslide<3->
471         Particle movement as a result of
472         \begin{itemize}
473            \item advection, resolved turbulence $\vec{V}_{i_{\text{resolved}}}$
474            \vspace{-2mm}
475            \item and subgrid turbulence $\vec{V}_{i_{\text{subgrid}}}$
476         \end{itemize}
477      \end{column}
478   \end{columns}
479   
480   \begin{tikzpicture}[remember picture, overlay]
481      \node [shift={(6 cm,-6.3cm)}]  at (current page.north west)
482         {%
483         \begin{tikzpicture}[remember picture, overlay]
484            \uncover<4->{\draw[->, ultra thick] (-2.05,0) -- (-5,-0.8);
485            \node[text width=14em] at (-3.2,-1.5) {\scriptsize $=0$, if \texttt{use\underline{ }sgs\underline{ }for\underline{ }particles = .F.} (default value)\\};}
486            \uncover<5->{\draw[->, ultra thick] (-1.95,0) -- (0,-0.8);
487            \node[text width=20em] at (3.2,-1.5) {\scriptsize $\ne0$, if \texttt{use\underline{ }sgs\underline{ }for\underline{ }particles = .T.}\\ determination of the subgrid part of the particle velocity as a solution of a stochastic differential equation\\};
488            \node[text width=14em] at (2.5,-2.5) {\scriptsize requires initialization parameter \texttt{use\underline{ }upstream\underline{ }for\underline{ }tke = .T.}\\ };}
489         \end{tikzpicture}
490         };
491    \end{tikzpicture}
492
493\end{frame}
494
495% Folie 9
496\begin{frame}[t]
497   \frametitle{Basic Particle Parameters (VI)}
498   \small
499   \vspace{-2mm}
500   Parameter \texttt{dt\underline{ }sort\underline{ }particles} that improves the performance of a simulation with (many) particles:
501
502   \onslide<2->
503   \begin{tikzpicture}[remember picture, overlay]
504      \node [shift={(1 cm,2.5cm)}]  at (current page.south west)
505         {%
506         \begin{tikzpicture}[remember picture, overlay]
507            \node at (2.5,4.2) {$t=t_0$:};
508            \draw[-] (0,0) -- (5,0);
509            \draw[-] (0,1) -- (5,1);
510            \draw[-] (0,2) -- (5,2);
511            \draw[-] (0,3) -- (5,3);
512            \draw[-] (0,0) -- (0,4);
513            \draw[-] (1,0) -- (1,4);           
514            \draw[-] (2,0) -- (2,4);             
515            \draw[-] (3,0) -- (3,4);
516            \draw[-] (4,0) -- (4,4);           
517            \draw[-] (5,4) -- (5,0);
518            \draw[-] (0,4) -- (5,4);
519           
520            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (0.25,0.5) {};
521            \node[scale=0.8] at (rd1) {1};
522            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (0.75,0.5) {};
523            \node[scale=0.8] at (rd2) {2};
524            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (1.25,0.5) {};
525            \node[scale=0.8] at (rd3) {3};
526            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (1.75,0.5) {};
527            \node[scale=0.8] at (rd4) {4};     
528            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (2.25,0.5) {};
529            \node[scale=0.8] at (rd5) {5};
530            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (2.75,0.5) {};
531            \node[scale=0.8] at (rd6) {6};   
532            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (3.25,0.5) {};
533            \node[scale=0.8] at (rd7) {7};
534            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (3.75,0.5) {};
535            \node[scale=0.8] at (rd8) {8};     
536            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (4.25,0.5) {};
537            \node[scale=0.8] at (rd9) {9};
538            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (4.75,0.5) {};
539            \node[scale=0.8] at (rd10) {10};
540            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (0.25,2.5) {};
541            \node[scale=0.8] at (rd11) {11};
542            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (0.75,2.5) {};
543            \node[scale=0.8] at (rd12) {12};
544            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd13) at (1.25,2.5) {};
545            \node[scale=0.8] at (rd13) {13};
546            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd14) at (1.75,2.5) {};
547            \node[scale=0.8] at (rd14) {14};     
548            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd15) at (2.25,2.5) {};
549            \node[scale=0.8] at (rd15) {15};
550            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd16) at (2.75,2.5) {};
551            \node[scale=0.8] at (rd16) {16};   
552            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd17) at (3.25,2.5) {};
553            \node[scale=0.8] at (rd17) {17};
554            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd18) at (3.75,2.5) {};
555            \node[scale=0.8] at (rd18) {18};     
556            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd19) at (4.25,2.5) {};
557            \node[scale=0.8] at (rd19) {19};
558            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd20) at (4.75,2.5) {};
559            \node[scale=0.8] at (rd20) {20}
560                   
561            \node[text width=14em] at (2.5,-0.9) {\scriptsize Particles are sorted in a way that their order follows the order in which the grid point values are stored (beneficial as the code contains many loops over all particles)\\};
562
563         \end{tikzpicture}
564         };
565      \uncover<3->{
566      \node [shift={(7 cm,2.5cm)}]  at (current page.south west)
567         {%
568         \begin{tikzpicture}[remember picture, overlay]
569
570            \node at (2.5,4.2) {$t>t_0$:};
571            \draw[-] (0,0) -- (5,0);
572            \draw[-] (0,1) -- (5,1);
573            \draw[-] (0,2) -- (5,2);
574            \draw[-] (0,3) -- (5,3);
575            \draw[-] (0,0) -- (0,4);
576            \draw[-] (1,0) -- (1,4);           
577            \draw[-] (2,0) -- (2,4);             
578            \draw[-] (3,0) -- (3,4);
579            \draw[-] (4,0) -- (4,4);           
580            \draw[-] (5,4) -- (5,0);
581            \draw[-] (0,4) -- (5,4);
582           
583            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (1.75,1.3) {};
584            \node[scale=0.8] at (rd1) {1};
585         
586            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (1.2,2.3) {};
587            \node[scale=0.8] at (rd2) {2};
588            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (2.3,2.3) {};
589            \node[scale=0.8] at (rd3) {3};
590            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (3.25,1.21) {};
591            \node[scale=0.8] at (rd4) {4};     
592            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (3.2,2.7) {};
593            \node[scale=0.8] at (rd5) {5};
594            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (3.25,1.7) {};
595            \node[scale=0.8] at (rd6) {6};   
596            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (1.25,1.6) {};
597            \node[scale=0.8] at (rd7) {7};
598            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (3.7,0.5) {};
599            \node[scale=0.8] at (rd8) {8};     
600            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (3.77,1.8) {};
601            \node[scale=0.8] at (rd9) {9};
602            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (2.6,1.3) {};
603            \node[scale=0.8] at (rd10) {10};
604            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (2.7,0.7) {};
605            \node[scale=0.8] at (rd11) {11};
606            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (0.21,1.3) {};
607            \node[scale=0.8] at (rd12) {12};
608            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd13) at (0.3,2.5) {};
609            \node[scale=0.8] at (rd13) {13};
610            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd14) at (1.75,2.5) {};
611            \node[scale=0.8] at (rd14) {14};     
612            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd15) at (2.3,1.7) {};
613            \node[scale=0.8] at (rd15) {15};
614            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd16) at (2.4,2.8) {};
615            \node[scale=0.8] at (rd16) {16};   
616            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd17) at (4.23,0.7) {};
617            \node[scale=0.8] at (rd17) {17};
618            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd18) at (3.77,2.6) {};
619            \node[scale=0.8] at (rd18) {18};     
620            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd19) at (4.23,3.3) {};
621            \node[scale=0.8] at (rd19) {19};
622            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd20) at (3.75,1.23) {};
623            \node[scale=0.8] at (rd20) {20}
624           
625            \node[text width=14em] at (2.5,-1.05) {\scriptsize By default, particles are not sorted after every time step, particles with subsequent numbers will need information from quite different LES grid points\\ \textcolor{red}{Bad cache utilization}\\};
626            \node at (-0.2,-1.9) {$\rightarrow$};
627         \end{tikzpicture}
628         };}
629   \end{tikzpicture} 
630\end{frame}
631
632% Folie 10
633\begin{frame}[t]
634   \frametitle{Basic Particle Parameters (VI)}
635   \small
636   \vspace{-2mm}
637   Parameter \texttt{dt\underline{ }sort\underline{ }particles} that improves the performance of a simulation with (many) particles:
638
639   \begin{tikzpicture}[remember picture, overlay]
640      \node [shift={(1 cm,2.5cm)}]  at (current page.south west)
641         {%
642         \begin{tikzpicture}[remember picture, overlay]
643            \node[text width=14em] at (2.5,3.8) {Higher performance with\\ resorting of particles:\\};
644            \uncover<2->{\node[text width=14em] at (2.5,1.6) {\scriptsize Temporal interval between the\\ sorting of particles determined\\ by the parameter\\ \ \\ \texttt{dt\underline{ }sort\underline{ }particles}\\ \ \\ (default value 0.0, i.e. particles are resorted at every time step)};} 
645            \uncover<3->{\node[text width=28em] at (5,-0.9) {Keep in mind that resorting of particles is time consuming itself, so that using the default value of \texttt{dt\underline{ }sort\underline{ }particles} probably won‘t yield the best performance that is possible.\\};}
646         \end{tikzpicture}
647         };
648      \node [shift={(7 cm,2.5cm)}]  at (current page.south west)
649         {%
650         \begin{tikzpicture}[remember picture, overlay]
651
652            \node at (2.5,4.2) {$t>t_0$:};
653            \draw[-] (0,0) -- (5,0);
654            \draw[-] (0,1) -- (5,1);
655            \draw[-] (0,2) -- (5,2);
656            \draw[-] (0,3) -- (5,3);
657            \draw[-] (0,0) -- (0,4);
658            \draw[-] (1,0) -- (1,4);           
659            \draw[-] (2,0) -- (2,4);             
660            \draw[-] (3,0) -- (3,4);
661            \draw[-] (4,0) -- (4,4);           
662            \draw[-] (5,4) -- (5,0);
663            \draw[-] (0,4) -- (5,4);
664           
665            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (1.75,1.3) {};
666            \node[scale=0.8] at (rd1) {1};
667         
668            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (1.2,2.3) {};
669            \node[scale=0.8] at (rd2) {2};
670            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (2.3,2.3) {};
671            \node[scale=0.8] at (rd3) {3};
672            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (3.25,1.21) {};
673            \node[scale=0.8] at (rd4) {4};     
674            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (3.2,2.7) {};
675            \node[scale=0.8] at (rd5) {5};
676            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (3.25,1.7) {};
677            \node[scale=0.8] at (rd6) {6};   
678            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (1.25,1.6) {};
679            \node[scale=0.8] at (rd7) {7};
680            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (3.7,0.5) {};
681            \node[scale=0.8] at (rd8) {8};     
682            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (3.77,1.8) {};
683            \node[scale=0.8] at (rd9) {9};
684            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (2.6,1.3) {};
685            \node[scale=0.8] at (rd10) {10};
686            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (2.7,0.7) {};
687            \node[scale=0.8] at (rd11) {11};
688            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (0.21,1.3) {};
689            \node[scale=0.8] at (rd12) {12};
690            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd13) at (0.3,2.5) {};
691            \node[scale=0.8] at (rd13) {13};
692            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd14) at (1.75,2.5) {};
693            \node[scale=0.8] at (rd14) {14};     
694            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd15) at (2.3,1.7) {};
695            \node[scale=0.8] at (rd15) {15};
696            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd16) at (2.4,2.8) {};
697            \node[scale=0.8] at (rd16) {16};   
698            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd17) at (4.23,0.7) {};
699            \node[scale=0.8] at (rd17) {17};
700            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd18) at (3.77,2.6) {};
701            \node[scale=0.8] at (rd18) {18};     
702            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd19) at (4.23,3.3) {};
703            \node[scale=0.8] at (rd19) {19};
704            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd20) at (3.75,1.23) {};
705            \node[scale=0.8] at (rd20) {20}
706         \end{tikzpicture}
707         };
708   \end{tikzpicture} 
709\end{frame}
710
711% Folie 11
712\begin{frame}[t]
713   \frametitle{Basic Particle Parameters (VI)}
714   \small
715   Example for the beneficial effect of resorting on the consumption of CPU time \texttt{(dt\underline{ }sort\underline{ }particles = 0.0)}:\\
716   \scriptsize \ \\
717   Release of 3.200.000 particles into a convective boundary layer.\\
718   Extract from CPU time measurement file.\\
719   \ \\
720
721   \begin{tabular}{|p{2.5cm}|p{1.3cm}|p{1.3cm}|p{1.3cm}|p{1.3cm}|p{1.3cm}|}
722      \hline
723           Part of PALM & Consumed CPU time in s \textbf{without resorting} & Percentage of totally consumed CPU time \textbf{(without)} & Consumed CPU time in s \textbf{with resorting}  & Percentage of totally consumed CPU time \textbf{(with)} & Saved CPU time \textbf{with resorting} in \%\\
724      \hline
725           total & 50027.225 & 100.0 & 47805.635  & 100.0 & \textcolor{red}{4.4}\\
726      \hline
727           advec\underline{ }particles & 22049.711 & 44.08 & 19926.364  & 41.68  & \textcolor{red}{9.6}\\
728      \hline
729           advec\underline{ }particles\underline{ }advec & 13640.729 & 27.27 & 11424.540  & 23.90  & \textcolor{red}{16.2}\\
730      \hline
731   \end{tabular}
732
733
734\end{frame}
735
736% Folie 12
737\begin{frame}[t]
738   \frametitle{Basic Particle Parameters (VII)}
739   \small
740   \vspace{-2mm}
741   Parameters that define the boundary conditions for particles\\
742   \scriptsize \ \\
743   \uncover<10>{In PALM particles are \textbf{always} reflected at \textbf{vertical walls and roofs of buildings.}}\\
744   \ \\
745
746   \begin{tikzpicture}
747      \definecolor{darkgreen}{rgb}{0.2,0.7,0.2}
748      % Bottom
749      \uncover<2>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
750         (0,0) --
751         (2,1.5) --
752         (7,1.5) --
753         (5,0) -- cycle ;}
754      % Top
755      \uncover<4>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
756         (0,4) --
757         (2,5.5) --
758         (7,5.5) --
759         (5,4) -- cycle ;}
760      % Front
761      \uncover<6>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
762         (0,0) --
763         (0,4) --
764         (5,4) --
765         (5,0) -- cycle ;}
766      % Back
767      \uncover<6>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
768         (2,1.5) --
769         (7,1.5) --
770         (7,5.5) --
771         (2,5.5) -- cycle ;}
772      % Left
773      \uncover<8>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
774         (0,0) --
775         (0,4) --
776         (2,5.5) --
777         (2,1.5) -- cycle ;}
778      % Right
779      \uncover<8>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
780         (5,0) --
781         (5,4) --
782         (7,5.5) --
783         (7,1.5) -- cycle ;}
784         
785      % Draw Box 
786      \draw[-] (0,0) -- (5,0);
787      \draw[-] (0,0) -- (0,4);
788      \draw[-] (5,4) -- (5,0);
789      \draw[-] (0,4) -- (5,4);
790     
791      \draw[-] (2,1.5) -- (7,1.5);
792      \draw[-] (2,1.5) -- (2,5.5);
793      \draw[-] (7,5.5) -- (7,1.5);
794      \draw[-] (2,5.5) -- (7,5.5);
795     
796      \draw[-] (0,0) -- (2,1.5);
797      \draw[-] (5,0) -- (7,1.5);
798      \draw[-] (5,4) -- (7,5.5);
799      \draw[-] (0,4) -- (2,5.5);
800     
801      \node at (4,5) {\small Total model domain};
802     
803      % Labels
804      \uncover<2->{\node at (2.7,0.15) {\scriptsize \texttt{bc\underline{ }par\underline{ }b = 'reflect', 'absorb'}};} 
805      \uncover<4->{\node at (3.0,4.25) {\scriptsize \texttt{bc\underline{ }par\underline{ }t = 'absorb', 'reflect'}};}       
806      \uncover<6->{\node at (3.25,2.15) {\scriptsize \texttt{bc\underline{ }par\underline{ }ns = 'cyclic', 'reflect', 'absorb'}};}     
807      \uncover<8->{\node[text width=15.5em] at (7.7,3.7) {\scriptsize \texttt{bc\underline{ }par\underline{ }lr = 'cyclic', 'reflect',}\\ \texttt{\hspace{5em} 'absorb'}};}           
808
809               
810      % Draw coordinate system
811      \node at (9,2) [scale=1.0] {%
812      \begin{tikzpicture}
813         \draw[->] (0,0) -- (1,0);
814         \draw[->] (0,0) -- (0,1);
815         \draw[->] (0,0) -- (0.5,0.5);
816         \node at (-0.2,0.9) {z};
817         \node at (0.9,-0.2) {x};
818         \node at (0.65,0.3) {y};
819      \end{tikzpicture}
820      };
821     
822   \end{tikzpicture}
823   
824\end{frame}
825
826% Folie 13
827\begin{frame}
828   \frametitle{Basic Particle Parameters (VIII)}
829   \small
830   Parameters that steer the output of particle data
831   \begin{itemize}
832      \item There are two output files containing particle data:
833      \begin{itemize}
834         \item \texttt{DATA\underline{ }1D\underline{ }PTS\underline{ }NETCDF}:
835         \hspace{0.5em} contains particle time series, output\\ 
836         \hspace{11.0em}interval is controlled by parameter\\ 
837         \hspace{11.0em}\texttt{dt\underline{ }dopts}, one file for the total\\ 
838         \hspace{11.0em}domain, e.g. time series of the total\\
839         \hspace{11.0em}number of particles, mean particle\\
840         \hspace{11.0em}velocity, mean subgrid scale part of\\
841         \hspace{11.0em}the particle velocity, mean particle\\
842         \hspace{11.0em}location etc.
843         \vspace{1mm}
844         \item \texttt{DATA\underline{ }PRT\underline{ }NETCDF}:
845         \hspace{2.5em}contains \textbf{all} particle data (see slide\\
846         \hspace{11.0em}The Data Type Used for Particles),\\
847         \hspace{11.0em}output is controlled by\\
848         \hspace{11.0em}\texttt{dt\underline{ }write\underline{ }particle\underline{ }data},\\
849         \hspace{11.0em}one file per subdomain/PE
850      \end{itemize}
851   \end{itemize}
852\end{frame}
853
854% Folie 14
855\begin{frame}
856   \frametitle{An Example of a Particle NAMELIST}
857   \includegraphics[scale=0.3]{particle_model_figures/namelist.png}
858   \begin{itemize}
859      \item<2-> \small Several (up to 10) so called particle groups with different density ratio, radius, and starting positions can be defined by setting parameter number\underline{ }of\underline{ }particle\underline{ }groups to the required number of groups, and by assigning values for each particle groups to the respective parameters (e.g. density\underline{ }ratio = 0.001, 0.0, etc.)
860   \end{itemize}
861\end{frame}
862
863% Folie 15
864\begin{frame}[t]
865   \frametitle{Theory of the Lagrangian Particle Model (I)}
866   \textbf{Advection of Passive particles}\\
867   \small
868   \vspace{1mm}
869   The position of a particle is found by integrating $ \dfrac{dX_{\text{particle}}}{dt} = \vec{V}_{\text{particle}}$\\
870   \vspace{2mm}
871   \onslide<2->Transferring the LES concept ...
872   \includegraphics[scale=0.1]{particle_model_figures/basic_particle_parameters_5.png}\\
873   \vspace{-2mm}
874   \scriptsize \hspace{2em}total energy\hspace{2.25em}=\hspace{3em}resolved part\hspace{2.5em}+\hspace{3em}modelled part\\
875   \vspace{1mm}
876   \small ... to the embedded particle model leads to: $\vec{V}_{\text{particle}} = \vec{V}_{\text{res}} (+ \vec{V}_{\text{sub}})$\\
877   \vspace{2mm}
878   \onslide<3->$\vec{V}_{\text{res}}:$\\ 
879   \begin{tikzpicture}[remember picture, overlay]
880      \node [shift={(1.7 cm,0.6cm)}]  at (current page.south west)
881         {%   
882         \begin{tikzpicture}[scale=0.3,remember picture, overlay]
883            \draw[-] (0,0) -- (5,0);
884            \draw[-] (0,0) -- (0,4);
885            \draw[-] (5,4) -- (5,0);
886            \draw[-] (0,4) -- (5,4);
887            \draw[-] (2,1.5) -- (7,1.5);
888            \draw[-] (2,1.5) -- (2,5.5);
889            \draw[-] (7,5.5) -- (7,1.5);
890            \draw[-] (2,5.5) -- (7,5.5);
891            \draw[-] (0,0) -- (2,1.5);
892            \draw[-] (5,0) -- (7,1.5);
893            \draw[-] (5,4) -- (7,5.5);
894            \draw[-] (0,4) -- (2,5.5);
895     
896            \node[circle, fill=blue, scale=0.5] at (0,0) {};
897            \node[circle, fill=blue, scale=0.5] at (5,0) {};
898            \node[circle, fill=blue, scale=0.5] at (0,4) {};
899            \node[circle, fill=blue, scale=0.5] at (5,4) {};
900            \node[circle, fill=blue, scale=0.5] at (2,1.5) {};
901            \node[circle, fill=blue, scale=0.5] at (7,1.5) {};
902            \node[circle, fill=blue, scale=0.5] at (7,5.5) {};
903            \node[circle, fill=blue, scale=0.5] at (2,5.5) {};
904     
905            \node[circle, fill=red, scale=0.5] at (2.5,1.1) {};
906
907            \draw[->, ultra thick, color=red] (7.4,0.7) -- (2.9,1.1);
908            \node at (9.0,0.1) {\scriptsize \textcolor{red}{particle location}};
909     
910            \draw[->, ultra thick] (8,2.5) -- (12,2.5);
911         \end{tikzpicture}
912         };
913      \node [shift={(5.8 cm,0.6cm)}]  at (current page.south west)
914         {%   
915         \begin{tikzpicture}[scale=0.3,remember picture, overlay]
916            \definecolor{darkgreen}{rgb}{0.2,0.7,0.2}
917            \draw[-] (0,0) -- (5,0);
918            \draw[-] (0,4) -- (5,4);
919            \draw[-] (2,1.5) -- (7,1.5);
920            \draw[-] (2,5.5) -- (7,5.5);
921            \draw[-] (0,0) -- (2,1.5);
922            \draw[-] (5,0) -- (7,1.5);
923            \draw[-] (5,4) -- (7,5.5);
924            \draw[-] (0,4) -- (2,5.5);
925     
926            \node[circle, fill=blue, scale=0.5] at (0,0) {};
927            \node[circle, fill=blue, scale=0.5] at (5,0) {};
928            \node[circle, fill=blue, scale=0.5] at (0,4) {};
929            \node[circle, fill=blue, scale=0.5] at (5,4) {};
930            \node[circle, fill=blue, scale=0.5] at (2,1.5) {};
931            \node[circle, fill=blue, scale=0.5] at (7,1.5) {};
932            \node[circle, fill=blue, scale=0.5] at (7,5.5) {};
933            \node[circle, fill=blue, scale=0.5] at (2,5.5) {};
934           
935            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,0.6) {};       
936            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,4.6) {};         
937            \draw[->, ultra thick] (8,2.5) -- (12,2.5);
938         \end{tikzpicture}
939         };
940      \node [shift={(9 cm,0.6cm)}]  at (current page.south west)
941         {%   
942         \begin{tikzpicture}[scale=0.3,remember picture, overlay]
943            \definecolor{darkgreen}{rgb}{0.2,0.7,0.2}
944           
945            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,0.6) {};       
946            \node[circle, fill=red, scale=0.5] at (2.5,1.1) {};
947            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,4.6) {};         
948         \end{tikzpicture}
949         };
950      \end{tikzpicture}
951\end{frame}
952
953% Folie 16
954\begin{frame}[t]
955   \frametitle{Theory of the Lagrangian Particle Model (II)}
956   \scriptsize \textbf{A: Passive particles}\\
957   \ \\
958   \uncover<10->{\normalsize \textbf{\underline{Calculation of the subgrid part of the particle velocity $\vec{V}_{\text{sub}}$:}}}
959   \footnotesize
960   \begin{itemize}
961      \item<3-> Application of the method of Weil et al. (2004)
962      \item<2-> \uncover<4->{they derived an adaptation of Thomson's model (1987)}\\
963      \vspace{1mm}
964      \uncover<2->{$\dfrac{dV_{\text{particle}_i}}{dt} = a_i dt + (C_0 \overline{\varepsilon})^{\frac{1}{2}} d \xi_i$ \quad deterministic + random velocity forcing}\\
965      \vspace{1mm}
966      \uncover<5->{to the grid-volume level, i.e.:}
967      \item<6-> Ensemble-mean velocity replaced by the LES resolved velocity
968      \item<7-> Lagrangian stochastic model describes the subgrid scale random velocity fluctuation about the resolved velocity
969      \item<8-> The subgrid scale velocities are specified by a Gaussian probability density function based on the subgrid scale stress tensor and its inverse
970      \item<9-> The ensemble mean dissipation rate can be replaced by the local dissipation rate     
971   \end{itemize}
972\end{frame}
973
974% Folie 17
975\begin{frame}[t]
976   \frametitle{Theory of the Lagrangian Particle Model (III)}
977   \scriptsize \textbf{A: Passive particles}\\
978   \ \\
979   \normalsize \textbf{\underline{Weil's formula for the subgrid part of the particle velocity:}}
980   \footnotesize \\
981   \vspace{2mm}
982   Assumption: subgrid scale turbulence locally isotropic\\
983   \vspace{6mm}
984   $dV_{\text{sub}_i} = - \dfrac{3 f_s C_0}{4} \dfrac{V_{\text{sub}_i}}{e_s} dt + \dfrac{1}{3} \left( \dfrac{\partial e_s}{\partial x_i} + \dfrac{3}{2 e_s} \dfrac{d e_s}{dt} V_{\text{sub}_i}\right) dt + \sqrt{f_s C_0 \varepsilon}\, d\xi_i$\\
985   \vspace{2mm}
986   $f_s = \dfrac{\langle 2 e_s / 3 \rangle}{\langle 2 e_s / 3 \rangle + \langle \left( \sigma^2_{\text{res}U} + \sigma^2_{\text{res}V} + \sigma^2_{\text{res}W} \right) /3 \rangle}$\\
987   \vspace{6mm}
988   Local dissipation rate $\varepsilon$ , subgrid scale turbulent kinetic energy $e_s$ and variances of resolved velocity components $\sigma_{\text{res}_i}$ derived from LES data\\
989\end{frame}
990
991% Folie 18
992\begin{frame}[t]
993   \frametitle{Theory of the Lagrangian Particle Model (IV)}
994   \scriptsize \textbf{A: Passive particles}\\
995   \ \\
996   \normalsize \textbf{\underline{Particle time step in case of \texttt{use\underline{ }sgs\underline{ }for\underline{ }particles = .TRUE.}:}}
997   \footnotesize \\
998   \vspace{2mm}
999   limited by the Lagrangian time scale $T_L$ \qquad $dt=0.025 T_L$\\
1000   \vspace{3mm}
1001   subsequent particle time steps: velocities correlated, accelerations not correlated\\
1002   \vspace{3mm}
1003   Lagrangian autocorrelation function:\\
1004   \begin{tikzpicture}[domain=0:4]
1005      \draw[->] (0,0) -- (4.5,0);
1006      \draw[->] (0,0) -- (0,2);
1007      \node at (4.5,-0.3) {$\tau$};
1008      \node at (-0.5,1.8) {$R_L(\tau)$};
1009      \draw[thick, domain=0:4] plot (\x,{1.7*exp(-1.6*\x)+0.05});
1010   \end{tikzpicture}\\
1011   $R_L(\tau) = \dfrac{W(t) W(t + \tau)}{\sigma^2_w} = exp\left( - \dfrac{\tau}{T_L} \right) \hspace{10mm} T_L = 4 e_s / (3 f_s C_0 \varepsilon)$\\
1012   \ \\
1013   Particle time step can be smaller than LES time step!
1014\end{frame}
1015
1016% Folie 19
1017\begin{frame}[t]
1018   \frametitle{Theory of the Lagrangian Particle Model (V)}
1019   \scriptsize \textbf{B: Non-passive particles (e.g. cloud droplets) }\\
1020   \ \\
1021   \footnotesize
1022   $\rightarrow$ advection of particles by the non-linear drag law following Clift et al., 1978\\
1023   \vspace{4mm}
1024   \onslide<2->$\dfrac{dV_i}{dt} = \dfrac{1}{\tau_p} (u_i - V_i -\delta_{i3}w_s) \rightarrow V_i(t) = V_i(0) e^{-\Delta t / \tau_p} + (u_i -w_s \delta_{i3}) \left( 1 - e^{-\Delta t / \tau_p} \right)$\\
1025      \vspace{2mm}
1026   with $\tau_p^{-1} = \dfrac{3 \pi}{8 \beta r} C_D \left| \vec{u} - \vec{V} \right|$, $C_D = \dfrac{24}{\text{Re}} \left( 1 + 0.15 \text{Re}^{0.687} \right)$, $w_s = \dfrac{\beta -1}{\beta} g \tau_p$,\\ \vspace{1mm} \hspace{2em} $\beta = \dfrac{\rho_p}{\rho_f}$\\
1027   \vspace{5mm}
1028   \onslide<1->
1029   \begin{tabular}{llll}
1030           $C_D$ & = drag coefficient           & $w_s$    & = terminal velocity\\
1031           $g$   & = gravitational acceleration & $\beta$  & = density coefficient\\
1032           Re    & = Reynolds number            & $\rho_p$ & = density of the particle\\
1033           $u_i$ & = velocity of the fluid      & $\rho_f$ & = density of the fluid\\
1034           $V_i$ & = particle velocity          & $\tau_p$ & = response time with respect to inertia\\
1035   \end{tabular}
1036\end{frame}
1037
1038
1039% Folie 20
1040\begin{frame}
1041   \frametitle{Flow Chart of Particle Code (I)}
1042   \footnotesize
1043   \begin{tikzpicture}[scale=0.8, transform shape]
1044      % Define colours
1045      \tikzstyle{gelb1} = [draw, fill=yellow!60, text width=7em, text centered, minimum height=1.6em]
1046      \tikzstyle{orange} = [draw, fill=orange!60, text width=7em, text centered]
1047     
1048      % Define coordinates and draw nodes     
1049      \node[gelb1, text width=5em] (PALM) at (0,0.1) {PALM};
1050
1051      \coordinate (A) at (0,-0.7);
1052
1053      \node[gelb1, right=0.6cm of A] (init3d) {init\underline{ }3d\underline{ }model};
1054     
1055      \coordinate[below=0.4cm of init3d] (B) ;
1056      \coordinate[below=1.0cm of init3d] (C) ;       
1057      \coordinate[below=1.6cm of init3d] (D) ;       
1058      \coordinate[below=2.2cm of init3d] (E) ;       
1059      \coordinate[below=2.8cm of init3d] (F) ;       
1060      \coordinate[below=4.2cm of init3d] (G) ;     
1061      \coordinate[below=4.8cm of init3d] (H) ;     
1062      \coordinate[below=7cm of init3d] (I) ;   
1063      \coordinate (J) at (0,-8.6);
1064           
1065      \node[gelb1, right=0.5cm of B, text width=17em] (init1d) {init\underline{ }1d\underline{ }model (\textit{calls various subroutines})};
1066      \node[gelb1, right=0.5cm of C] (initslope) {init\underline{ }slope};
1067      \node[gelb1, right=0.5cm of D] (disturb) {disturb\underline{ }heatflux};
1068      \node[gelb1, right=0.5cm of E] (initrankine) {init\underline{ }rankine};
1069      \node[gelb1, right=0.0cm of initrankine] {init\underline{ }pt\underline{ }anomaly};
1070      \node[gelb1, right=0.5cm of F] (disturbfield) {disturb\underline{ }field};
1071      \node[gelb1, right=0.0cm of disturbfield] (pres) {pres};
1072      \node[gelb1, right=0.5cm of G] (read3d) {read\underline{ }3d\underline{ }binary};
1073      \node[gelb1, right=0.0cm of read3d] (initdvrp) {init\underline{ }dvrp};
1074      \node[gelb1, right=0.0cm of initdvrp] (initocean) {init\underline{ }ocean};
1075      \node[gelb1, right=0.0cm of initocean] {init\underline{ }cloud\underline{ }physics};           
1076      \node[orange, right=0.5cm of H] (initparticles) {init\underline{ }particles};     
1077      \node[gelb1, right=0.5cm of I] (initadvec) {init\underline{ }advec};     
1078      \node[gelb1, right=0.0cm of initadvec] (userinit) {user\underline{ }init};
1079      \node[gelb1, right=0.6cm of J] (dataoutput2d) {data\underline{ }output\underline{ }2d};     
1080      \node[gelb1, right=0.0cm of dataoutput2d] {data\underline{ }output\underline{ }3d};         
1081
1082      \coordinate[below=0.15cm of pres] (K);
1083      \coordinate[right=0.2cm of K] (L);
1084      \coordinate[right=2cm of L] (M);
1085      \coordinate[right=2cm of M] (N);
1086           
1087      \node[gelb1, below=0.1cm of L, text width=4em] (poisfft) {poisfft};
1088      \node[gelb1, below=0.1cm of M, text width=4em] (sor) {sor};
1089      \node[gelb1, below=0.1cm of N, text width=4em] (poismg) {poismg};
1090     
1091      \coordinate[below=0.1cm of initparticles] (O);
1092      \coordinate[below=0.6cm of O] (P);
1093      \coordinate[below=0.6cm of P] (Q);
1094     
1095      \node[orange, right=1.5cm of O] (userinitparticles) {user\underline{ }init\underline{ }particles};
1096      \node[orange, right=1.5cm of P] (sortparticles) {sort\underline{ }particles};
1097      \node[orange, right=1.5cm of Q] (dataoutputdvrp) {data\underline{ }output\underline{ }dvrp};
1098     
1099      \coordinate[right=1.5cm of dataoutputdvrp] (R);
1100
1101      \node[orange, below=0.3cm of R] (userdvrp) {user\underline{ }dvrp\underline{ }coltab};
1102   
1103      % Draw lines 
1104      \draw[dotted, thick] (PALM) -- (0,-0.5);
1105      \draw[-, thick] (0,-0.5) -- (0,-8.7);
1106      \draw[dotted, thick] (0,-8.7) -- (0,-9.0);     
1107      \draw[-, thick] (init3d.west) -- (A) ;
1108      \draw[-, thick] (init3d.south) -- (I) ;
1109      \draw[dashed, thick] (B) -- (init1d.west);
1110      \draw[dashed, thick] (C) -- (initslope.west);
1111      \draw[dashed, thick] (D) -- (disturb.west);
1112      \draw[dashed, thick] (E) -- (initrankine.west);
1113      \draw[dashed, thick] (F) -- (disturbfield.west);
1114      \draw[dashed, thick] (G) -- (read3d.west);     
1115      \draw[-, thick] (H) -- (initparticles.west);     
1116      \draw[-, thick] (I) -- (initadvec.west);         
1117      \draw[dashed, thick] (J) -- (dataoutput2d);     
1118      \draw[-, thick] (pres.south) -- (K);
1119      \draw[-, thick] (K) -- (N);
1120      \draw[-, thick] (L) -- (poisfft.north);
1121      \draw[-, thick] (M) -- (sor.north);     
1122      \draw[-, thick] (N) -- (poismg.north);       
1123      \draw[-, thick] (initparticles.south) -- (P);
1124      \draw[dashed, thick] (P) -- (Q);
1125      \draw[-, thick] (O) -- (userinitparticles.west);
1126      \draw[-, thick] (P) -- (sortparticles.west);
1127      \draw[dashed, thick] (Q) -- (dataoutputdvrp.west);           
1128      \draw[-, thick] (dataoutputdvrp.east) -- (R);
1129      \draw[-, thick] (R) -- (userdvrp.north);
1130     
1131   \end{tikzpicture}
1132   
1133   
1134\end{frame}
1135
1136% Folie 21
1137\begin{frame}
1138   \frametitle{Flow Chart of Particle Code (II)}
1139   \footnotesize
1140   \begin{tikzpicture}[scale=0.8, transform shape]
1141      % Define colours
1142      \tikzstyle{gelb1} = [draw, fill=yellow!60, text width=7em, text centered, minimum height=1.6em]
1143      \tikzstyle{orange} = [draw, fill=orange!60, text width=7em, text centered]
1144     
1145      % Define coordinates and draw nodes
1146      \coordinate (A) at (0,-0.7);
1147
1148      \node[gelb1, right=0.6cm of A] (timeintegration) {time\underline{ }integration};
1149     
1150      \coordinate[below=0.3 of timeintegration] (B);
1151      \coordinate[below=0.9 of timeintegration] (C);
1152     
1153      \node[gelb1, right=0.6cm of B] (timestep) {timestep};
1154      \node[gelb1, right=0.6cm of C] (runcontrol) {run\underline{ }control};
1155     
1156      \coordinate[below=0.2cm of runcontrol] (D);
1157     
1158      \node[gelb1, right=1.5cm of D] (flowstat) {flow\underline{ }statistics};
1159     
1160      \coordinate[below=1.8cm of timeintegration] (E);
1161     
1162      \node[gelb1, right=0.6cm of E] (surface) {surface\underline{ }coupler};
1163     
1164      \coordinate[below=2.4cm of timeintegration] (F);
1165       
1166      \node[gelb1, right=0.6cm of F, text width=13em] (useractions) {user\underline{ }actions (\textit{before\underline{ }timestep})};   
1167 
1168       \coordinate[below=3.0cm of timeintegration] (G);
1169       
1170      \node[gelb1, right=0.6cm of G, text width=11em] (timestepscheme) {timestep\underline{ }scheme\underline{ }steering};       
1171     
1172      \coordinate[below=3.5cm of timeintegration] (H);
1173      \coordinate[right=2cm of H] (I);
1174      \coordinate[right=3.5cm of I] (J);
1175     
1176      \node[draw, text width=22em,minimum height=4.5em,fill=black!15] (progframe) at (5.75,-5.3) {};
1177      \node[draw, text width= 9.5em, right=0.5cm of progframe] {For details, see PALM Flow Chart (V).};
1178      \node[gelb1, below=0.3cm of I, text width=9em] (prog) {prognostic\underline{ }equations};     
1179      \node[gelb1, below=0.3cm of J, text width=10.5em] (progfast) {prognostic\underline{ }equations\underline{ }fast}
1180      \node[gelb1, below=0.1cm of progfast, text width=10.5em] (progvec) {prognostic\underline{ }equations\underline{ }vec};       
1181      \node[draw, fill=red, text width=4em] at (8.2,-4) {\textcolor{white}{standard advection}};
1182     
1183      \coordinate[below=5.5cm of timeintegration] (K);
1184     
1185      \node[orange, right=0.6cm of K] (advecparticles) {advec\underline{ }particles};             
1186     
1187      \coordinate[below=0.2cm of advecparticles] (L);
1188     
1189      \node[orange, right=1.5cm of L, text width=13em] (userparticlesatt) {user\underline{ }particle\underline{ }attributes + more};
1190     
1191      \coordinate[below=6.6cm of timeintegration] (M);
1192     
1193      \node[orange, right=0.6cm of M, text width=10em] (interaction) {interaction\underline{ }droplets\underline{ }ptq};     
1194
1195      \coordinate[below=7.2cm of timeintegration] (N);
1196     
1197      \node[gelb1, right=0.6cm of N] (asselin) {asselin\underline{ }filter};     
1198     
1199      \coordinate[below=7.8cm of timeintegration] (O);
1200     
1201      \node[gelb1, right=0.6cm of O] (boundary) {boundary\underline{ }conds};       
1202      \node[gelb1, right=0.0cm of boundary] {swap\underline{ }timelevel}
1203           
1204      \coordinate[below=8.4cm of timeintegration] (P);     
1205     
1206      \node[gelb1, right=0.6cm of P] (inflow) {inflow\underline{ }turbulence};
1207      \node[gelb1, right=0.0cm of inflow] {disturb\underline{ }field};
1208                                                     
1209      % Draw lines 
1210      \draw[dotted, thick] (0,-0.3) -- (0,-0.7);
1211      \draw[-, thick] (0,-0.7) -- (0,-7.7);
1212      \draw[dotted, thick] (0,-7.7) -- (0,-9.0);     
1213      \draw[-, thick] (A) -- (timeintegration);
1214      \draw[-, thick] (B) -- (timestep);
1215      \draw[-, thick] (C) -- (runcontrol);
1216      \draw[-, thick] (runcontrol.south) -- (D);
1217      \draw[-, thick] (D) -- (flowstat);
1218      \draw[dashed, thick] (E) -- (surface);
1219      \draw[-, thick] (F) -- (useractions);     
1220      \draw[-, thick] (G) -- (timestepscheme);
1221      \draw[-, thick] (H) -- (I);
1222      \draw[-, thick] (I) -- (prog.north);
1223      \draw[-, thick, color=red] (I) -- (J);       
1224      \draw[->, thick, color=red] (J) -- (progfast.north);
1225      \draw[dashed, thick] (K) -- (advecparticles);           
1226      \draw[-, thick] (advecparticles.south) -- (L);           
1227      \draw[-, thick] (L) -- (userparticlesatt.west);       
1228      \draw[dashed, thick] (M) -- (interaction.west); 
1229      \draw[dashed, thick] (N) -- (asselin.west);       
1230      \draw[-, thick] (O) -- (boundary.west); 
1231      \draw[dashed, thick] (P) -- (inflow.west);             
1232      \draw[-, thick] (timeintegration.south) -- (O); 
1233      \draw[dashed, thick] (O) -- (P); 
1234     
1235   \end{tikzpicture}   
1236   
1237\end{frame}
1238
1239
1240% Folie 22
1241\begin{frame}
1242   \frametitle{Detailed Flow Chart of \texttt{advec\underline{ }particles} (I)}
1243   \scriptsize
1244   \begin{tikzpicture}[scale=0.87, transform shape]
1245      \node (0) at (0,0) {};
1246      \uncover<2->{\node[draw, right=0.0cm of 0, text width=15em] {write particle data on file\\ \qquad binary (\texttt{PARTICLE\underline{ }DATA/})\\ \quad + NetCDF (\texttt{DATA\underline{ }PRT\underline{ }NETCDF/})};}
1247      \uncover<3->{\node[draw, right=0.0cm of 0, yshift=-0.9cm] {calculate exponential terms for particles groups with inertia};}
1248      \uncover<4->{\node[draw, right=0.0cm of 0, yshift=-1.5cm] {particle growth by condensation/evaporation and collision};}
1249      \uncover<5->{\node[draw, right=0.0cm of 0, yshift=-2.1cm] {If SGS-velocities are used: calculate gradients of TKE};}
1250      \uncover<6->{\node[draw, right=0.0cm of 0, yshift=-2.85cm, text width=29em] {timestep loop\\ (repeated, unless each particle has reached the LES timestep \texttt{dt\underline{ }3d})};}
1251      \uncover<7->{\node[draw, right=0.5cm of 0, yshift=-3.9cm, text width=36em] {for each particle:\\ - interpolate velocities and SGS quantities (SGS-velocities, Lagrangian timescale, etc.\\ - calculate the particle advection};}
1252      \uncover<8->{\node[draw, right=0.5cm of 0, yshift=-4.8cm] {calculate particle reflection from walls (subroutine \texttt{particle\underline{ }boundary\underline{ }conds})};}
1253      \uncover<9->{\node[draw, right=0.5cm of 0, yshift=-5.4cm] {user defined actions (subroutine \texttt{user\underline{ }advec\underline{ }particles})};}     
1254      \uncover<10->{\node[draw, right=0.5cm of 0, yshift=-6.0cm] {if necessary, release a new set of particles};}
1255      \uncover<11->{\node[draw, right=0.5cm of 0, yshift=-6.6cm] {particle exchange between the subdomains};}   
1256      \uncover<12->{\node[draw, right=0.5cm of 0, yshift=-7.2cm] {boundary conditions at bottom and top};}
1257      \uncover<13->{\node[draw, right=0.5cm of 0, yshift=-7.8cm] {delete, pack, and sort particles};}   
1258   \end{tikzpicture}
1259\end{frame}
1260
1261% Folie 23
1262\begin{frame}
1263   \frametitle{Detailed Flow Chart of \texttt{advec\underline{ }particles} (II)}
1264   \scriptsize
1265   \begin{tikzpicture}[auto, node distance=0]
1266      \node (0) at (0,0) {};
1267      \node[draw, right=0.0cm of 0] {In case of cloud droplets: calculate the liquid water content};
1268      \uncover<2->{\node[draw, right=0.0cm of 0, yshift=-0.6cm] {user defined setting of particle attributes (subroutine user\underline{ }particle\underline{ }attributes)};}
1269      \uncover<3->{\node[draw, right=0.0cm of 0, yshift=-1.2cm] {if necessary, add actual positions to the particle tails};}
1270      \uncover<4->{\node[draw, right=0.0cm of 0, yshift=-1.8cm] {write particle statistics on file \texttt{PARTICLE\underline{ }INFOS} (ASCII format)}}   
1271   \end{tikzpicture}
1272   \vspace{5mm}
1273   \small
1274   \begin{itemize}
1275      \item<5-> For a better modular structure, subroutine advec\underline{ }particles will be split into several subroutines in one of the next PALM releases.
1276   \end{itemize}
1277\end{frame}
1278
1279% Folie 24
1280\begin{frame}
1281   \frametitle{The Data Type Used for Particles}
1282   \small
1283   \begin{itemize}
1284      \item Particle data are stored in a FORTRAN derived data type:
1285   \end{itemize}
1286   \includegraphics[scale=0.3]{particle_model_figures/data_type.png}
1287\end{frame}
1288
1289% Folie 25
1290\begin{frame}
1291   \frametitle{How to Read netCDF Particle Data from an External Program}
1292   \footnotesize
1293   \begin{itemize}
1294      \item An example program for reading netCDF particle data (from file DATA\underline{ }PRT\underline{ }NETCDF/) can be found in the PALM repository under \texttt{...../trunk/UTIL/analyze\underline{ }particle\underline{ }netcdf\underline{ }data.f90}
1295       \item<2-> \textbf{Attention:}\\ The particle feature \grqq density\underline{ }ratio\grqq\, is stored in variable particle\underline{ }groups which (so far) is \textbf{not} contained in the netCDF file.\\ Also, informations about particle tails (history of particle positions) are \textbf{not} on the netCDF file!\\
1296       \vspace{1mm}
1297       Both informations can only be found on file PARTICLE\underline{ }DATA/.\\
1298       \vspace{1mm}
1299       For the format of this file (one per PE, i.e. filenames \underline{ }0000, \underline{ }0001, etc.) see beginning of subroutine advec\underline{ }particles.
1300   \end{itemize}
1301   \onslide<3->\hspace{4mm}\includegraphics[scale=0.27]{particle_model_figures/particle_data.png}
1302\end{frame}
1303
1304% Folie 26
1305\begin{frame}
1306   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (I)}
1307   \footnotesize
1308   \textbf{What is a footprint?}
1309   \begin{itemize}
1310      \item field of view of a micrometeorological measurement
1311   \end{itemize}
1312   \onslide<2->
1313   \textbf{What is the motivation for footprint modelling?}
1314   \begin{itemize}
1315      \item measured turbulent fluxes don’t represent the fluxes originating directly from below the measuring device, but rather represent the fluxes originating from an area upwind of the measuring device
1316   \end{itemize}
1317   \onslide<3->
1318   \textbf{How is it done?}
1319   \begin{itemize}
1320      \item particle trajectories are calculated in LES using embedded Lagrangian Particle Model
1321      \item once a particle intersects with chosen measuring height, footprint relevant data is output
1322      \item footprints are calculated in postprocessing
1323   \end{itemize}
1324   \onslide<4->
1325   \textbf{What to keep in mind?}
1326   \begin{itemize}
1327      \item including subgridscale particle velocities necessary, when calculating footprints close to the surface, where subgridscale contribution\\to turbulent kinetic energy is relatively large
1328   \end{itemize}
1329\end{frame}
1330
1331% Folie 27
1332\begin{frame}
1333   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (II)}
1334   \footnotesize
1335   \begin{center}
1336      \includegraphics[scale=0.4]{particle_model_figures/footprint2.png}
1337   \end{center}
1338   \vspace{-6mm}
1339   \begin{flushright}
1340      after Steinfeld, 2009
1341   \end{flushright}
1342\end{frame}
1343
1344% Folie 28
1345\begin{frame}
1346   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (III)}
1347   \footnotesize
1348   \textbf{Setup} (according to Steinfeld et al., 2008)
1349   \includegraphics[scale=0.285]{particle_model_figures/footprint3_1.png} \hspace{2mm}
1350   \includegraphics[scale=0.5]{particle_model_figures/footprint3_2.png}
1351   \begin{itemize}
1352      \item particles are released every 2min over a period of 30min at z=70m in the total model domain ($\rightarrow$ 7 * 106 particles)
1353      \item particles are measured at z=72.5m, 77.5m, 100.0m
1354   \end{itemize}
1355\end{frame}
1356
1357% Folie 29
1358\begin{frame}
1359   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (IV)}
1360   \footnotesize
1361   Extract from the corresponding parameter file:
1362   \includegraphics[scale=0.285]{particle_model_figures/footprint4.png}
1363\end{frame}
1364
1365% Folie 30
1366\begin{frame}
1367   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (V)}
1368   \footnotesize
1369   Additionally required user-defined code (continued):
1370   \begin{enumerate}
1371      \scriptsize
1372      \setcounter{enumi}{0}
1373      \item     Open files (one per PE and measuring height) for the additional output of footprint relevant particle data in \texttt{user\underline{ }init}
1374   \end{enumerate}
1375   \includegraphics[scale=0.27]{particle_model_figures/footprint5_1.png}
1376   \begin{enumerate}
1377      \scriptsize
1378      \setcounter{enumi}{1}
1379      \item Create directory into which the files containing the particle data shall be moved to and move the files (in .mrun.config)
1380   \end{enumerate}
1381   \includegraphics[scale=0.27]{particle_model_figures/footprint5_2.png}
1382\end{frame}
1383
1384% Folie 31
1385\begin{frame}
1386   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (VI)}
1387   \footnotesize
1388   Additionally required user-defined code (continued):
1389   \begin{enumerate}
1390      \scriptsize
1391      \setcounter{enumi}{2}
1392      \item Output of footprint relevant data in \texttt{user\underline{ }advec\underline{ }particles} (checking if particle has crossed measuring height)
1393   \end{enumerate}
1394   \includegraphics[scale=0.285]{particle_model_figures/footprint6.png}
1395\end{frame}
1396
1397% Folie 32
1398\begin{frame}
1399   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (VII)}
1400   \includegraphics[scale=0.3]{particle_model_figures/example1.png}
1401   \includegraphics[scale=0.35]{particle_model_figures/example2.png}\\
1402   \begin{itemize}
1403      \item sensor position at x = 0m
1404   \end{itemize}
1405\end{frame}
1406
1407% Folie 33
1408\begin{frame}
1409   \frametitle{Using Particles as Cloud Droplets}
1410   \begin{itemize}
1411      \item<1-> This feature is switched on by setting the initial parameter cloud\underline{ }droplets = \textit{.TRUE.}.
1412      \item<2-> In this case, the change in particle radius by condensation/evaporation and collision is calculated for every timestep.
1413      \item<3-> In case of condensation or evaporation, the potential temperature and the specific humidity has to be adjusted in the respective grid volumes. This is done within the subroutine interaction\underline{ }droplets\underline{ }ptq.
1414   \end{itemize}
1415\end{frame}
1416
1417% Folie 34
1418\begin{frame}
1419   \frametitle{General Warning}
1420   \begin{itemize}
1421      \item<2-> Errors in the user interface routines for particles may cause problems which are very difficult to debug. Please be extremely careful with modifying the user interface and try to find out exactly how the default particle code works, before you make your modifications.
1422   \end{itemize}
1423\end{frame}
1424
1425\end{document}
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