source: palm/trunk/TUTORIAL/SOURCE/particle_model.tex @ 1544

Last change on this file since 1544 was 954, checked in by maronga, 12 years ago

added/updated tutorial presentations

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1% $Id: particle_model.tex 954 2012-07-20 07:44:19Z hoffmann $
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            \onslide<3->
415            \draw[->, ultra thick, color=red] (5,0.5) -- (5,-0.5);
416            \node[text width=4em] at (4.8,-1.7) {\scriptsize Release of a new set of particles}
417            \node at (3.75,0.3) {\scriptsize \texttt{dt\underline{ }prel}};
418            \draw[<->, thick, color=blue] (2.5,0.6) -- (4.95,0.6);
419     
420            \onslide<4->
421            \draw[->, ultra thick, color=darkred] (6.5,0.5) -- (6.5,-0.5);   
422            \node[text width=5em] at (6.7,-1.7) {\scriptsize Deletion of the first set of particles};
423            \draw[<->, thick, color=darkred] (2.5,0.9) -- (6.5,0.9);
424            \node at (4.5,1.2) {\scriptsize \texttt{particle\underline{ }maximum\underline{ }age}};
425     
426            \onslide<5->
427            \draw[->, ultra thick, color=darkred] (8.5,0.5) -- (8.5,-0.5); 
428            \node[text width=5em] at (8.6,-1.9) {\scriptsize No release of new particles after this time};
429            \node at (8.5,-0.8) {\scriptsize \texttt{end\underline{ }time\underline{ }prel}};
430            \draw[<->, thick, color=blue] (5.05,0.6) -- (8.5,0.6);
431
432            \onslide<6->
433            \draw[->, ultra thick, color=grey] (10.2,0.5) -- (10.2,-0.5);     
434            \node[text width=5em] at (10.7,-1.9) {\scriptsize Deletion of the second set of particles};
435            \draw[<->, thick, color=darkred] (5.0,1.6) -- (10.2,1.6);
436           
437            \onslide<1->
438         \end{tikzpicture}
439       \end{column}
440   \end{columns}
441
442 
443\end{frame}
444
445% Folie 8
446\begin{frame}[t]
447   \frametitle{Basic Particle Parameters (V)}
448   \small
449   Parameter that defines the mode of particle movement: \\
450   The concept of LES ...\\
451   \vspace{-5mm}
452   \begin{center}
453      \includegraphics[scale=0.1]{particle_model_figures/basic_particle_parameters_5.png}
454   \end{center}
455   \vspace{-5mm}
456   \onslide<2->
457   ... transferred to the embedded particle model leads to particle velocity\\
458   \vspace{1mm}
459   \begin{columns}[T]
460      \begin{column}{0.35\textwidth}
461         $\vec{V}_{i_{\text{particle}}} = \vec{V}_{i_{\text{resolved}}} + \vec{V}_{i_{\text{subgrid}}}$
462      \end{column}
463      \begin{column}{0.55\textwidth}
464         \scriptsize
465         \onslide<3->
466         Particle movement as a result of
467         \begin{itemize}
468            \item advection, resolved turbulence $\vec{V}_{i_{\text{resolved}}}$
469            \vspace{-2mm}
470            \item and subgrid turbulence $\vec{V}_{i_{\text{subgrid}}}$
471         \end{itemize}
472      \end{column}
473   \end{columns}
474   
475   \begin{tikzpicture}[remember picture, overlay]
476      \node [shift={(6 cm,-6.3cm)}]  at (current page.north west)
477         {%
478         \begin{tikzpicture}[remember picture, overlay]
479            \uncover<4->{\draw[->, ultra thick] (-2.05,0) -- (-5,-0.8);
480            \node[text width=14em] at (-3.2,-1.5) {\scriptsize $=0$, if \texttt{use\underline{ }sgs\underline{ }for\underline{ }particles = .F.} (default value)\\};}
481            \uncover<5->{\draw[->, ultra thick] (-1.95,0) -- (0,-0.8);
482            \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\\};
483            \node[text width=14em] at (2.5,-2.5) {\scriptsize requires initialization parameter \texttt{use\underline{ }upstream\underline{ }for\underline{ }tke = .T.}\\ };}
484         \end{tikzpicture}
485         };
486    \end{tikzpicture}
487
488\end{frame}
489
490% Folie 9
491\begin{frame}[t]
492   \frametitle{Basic Particle Parameters (VI)}
493   \small
494   \vspace{-2mm}
495   Parameter \texttt{dt\underline{ }sort\underline{ }particles} that improves the performance of a simulation with (many) particles:
496
497   \onslide<2->
498   \begin{tikzpicture}[remember picture, overlay]
499      \node [shift={(1 cm,2.5cm)}]  at (current page.south west)
500         {%
501         \begin{tikzpicture}[remember picture, overlay]
502            \node at (2.5,4.2) {$t=t_0$:};
503            \draw[-] (0,0) -- (5,0);
504            \draw[-] (0,1) -- (5,1);
505            \draw[-] (0,2) -- (5,2);
506            \draw[-] (0,3) -- (5,3);
507            \draw[-] (0,0) -- (0,4);
508            \draw[-] (1,0) -- (1,4);           
509            \draw[-] (2,0) -- (2,4);             
510            \draw[-] (3,0) -- (3,4);
511            \draw[-] (4,0) -- (4,4);           
512            \draw[-] (5,4) -- (5,0);
513            \draw[-] (0,4) -- (5,4);
514           
515            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (0.25,0.5) {};
516            \node[scale=0.8] at (rd1) {1};
517            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (0.75,0.5) {};
518            \node[scale=0.8] at (rd2) {2};
519            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (1.25,0.5) {};
520            \node[scale=0.8] at (rd3) {3};
521            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (1.75,0.5) {};
522            \node[scale=0.8] at (rd4) {4};     
523            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (2.25,0.5) {};
524            \node[scale=0.8] at (rd5) {5};
525            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (2.75,0.5) {};
526            \node[scale=0.8] at (rd6) {6};   
527            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (3.25,0.5) {};
528            \node[scale=0.8] at (rd7) {7};
529            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (3.75,0.5) {};
530            \node[scale=0.8] at (rd8) {8};     
531            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (4.25,0.5) {};
532            \node[scale=0.8] at (rd9) {9};
533            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (4.75,0.5) {};
534            \node[scale=0.8] at (rd10) {10};
535            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (0.25,2.5) {};
536            \node[scale=0.8] at (rd11) {11};
537            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (0.75,2.5) {};
538            \node[scale=0.8] at (rd12) {12};
539            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd13) at (1.25,2.5) {};
540            \node[scale=0.8] at (rd13) {13};
541            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd14) at (1.75,2.5) {};
542            \node[scale=0.8] at (rd14) {14};     
543            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd15) at (2.25,2.5) {};
544            \node[scale=0.8] at (rd15) {15};
545            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd16) at (2.75,2.5) {};
546            \node[scale=0.8] at (rd16) {16};   
547            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd17) at (3.25,2.5) {};
548            \node[scale=0.8] at (rd17) {17};
549            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd18) at (3.75,2.5) {};
550            \node[scale=0.8] at (rd18) {18};     
551            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd19) at (4.25,2.5) {};
552            \node[scale=0.8] at (rd19) {19};
553            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd20) at (4.75,2.5) {};
554            \node[scale=0.8] at (rd20) {20}
555                   
556            \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)\\};
557
558         \end{tikzpicture}
559         };
560      \uncover<3->{
561      \node [shift={(7 cm,2.5cm)}]  at (current page.south west)
562         {%
563         \begin{tikzpicture}[remember picture, overlay]
564
565            \node at (2.5,4.2) {$t>t_0$:};
566            \draw[-] (0,0) -- (5,0);
567            \draw[-] (0,1) -- (5,1);
568            \draw[-] (0,2) -- (5,2);
569            \draw[-] (0,3) -- (5,3);
570            \draw[-] (0,0) -- (0,4);
571            \draw[-] (1,0) -- (1,4);           
572            \draw[-] (2,0) -- (2,4);             
573            \draw[-] (3,0) -- (3,4);
574            \draw[-] (4,0) -- (4,4);           
575            \draw[-] (5,4) -- (5,0);
576            \draw[-] (0,4) -- (5,4);
577           
578            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (1.75,1.3) {};
579            \node[scale=0.8] at (rd1) {1};
580         
581            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (1.2,2.3) {};
582            \node[scale=0.8] at (rd2) {2};
583            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (2.3,2.3) {};
584            \node[scale=0.8] at (rd3) {3};
585            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (3.25,1.21) {};
586            \node[scale=0.8] at (rd4) {4};     
587            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (3.2,2.7) {};
588            \node[scale=0.8] at (rd5) {5};
589            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (3.25,1.7) {};
590            \node[scale=0.8] at (rd6) {6};   
591            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (1.25,1.6) {};
592            \node[scale=0.8] at (rd7) {7};
593            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (3.7,0.5) {};
594            \node[scale=0.8] at (rd8) {8};     
595            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (3.77,1.8) {};
596            \node[scale=0.8] at (rd9) {9};
597            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (2.6,1.3) {};
598            \node[scale=0.8] at (rd10) {10};
599            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (2.7,0.7) {};
600            \node[scale=0.8] at (rd11) {11};
601            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (0.21,1.3) {};
602            \node[scale=0.8] at (rd12) {12};
603            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd13) at (0.3,2.5) {};
604            \node[scale=0.8] at (rd13) {13};
605            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd14) at (1.75,2.5) {};
606            \node[scale=0.8] at (rd14) {14};     
607            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd15) at (2.3,1.7) {};
608            \node[scale=0.8] at (rd15) {15};
609            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd16) at (2.4,2.8) {};
610            \node[scale=0.8] at (rd16) {16};   
611            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd17) at (4.23,0.7) {};
612            \node[scale=0.8] at (rd17) {17};
613            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd18) at (3.77,2.6) {};
614            \node[scale=0.8] at (rd18) {18};     
615            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd19) at (4.23,3.3) {};
616            \node[scale=0.8] at (rd19) {19};
617            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd20) at (3.75,1.23) {};
618            \node[scale=0.8] at (rd20) {20}
619           
620            \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}\\};
621            \node at (-0.2,-1.9) {$\rightarrow$};
622         \end{tikzpicture}
623         };}
624   \end{tikzpicture} 
625\end{frame}
626
627% Folie 10
628\begin{frame}[t]
629   \frametitle{Basic Particle Parameters (VI)}
630   \small
631   \vspace{-2mm}
632   Parameter \texttt{dt\underline{ }sort\underline{ }particles} that improves the performance of a simulation with (many) particles:
633
634   \begin{tikzpicture}[remember picture, overlay]
635      \node [shift={(1 cm,2.5cm)}]  at (current page.south west)
636         {%
637         \begin{tikzpicture}[remember picture, overlay]
638            \node[text width=14em] at (2.5,3.8) {Higher performance with\\ resorting of particles:\\};
639            \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)};} 
640            \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.\\};}
641         \end{tikzpicture}
642         };
643      \node [shift={(7 cm,2.5cm)}]  at (current page.south west)
644         {%
645         \begin{tikzpicture}[remember picture, overlay]
646
647            \node at (2.5,4.2) {$t>t_0$:};
648            \draw[-] (0,0) -- (5,0);
649            \draw[-] (0,1) -- (5,1);
650            \draw[-] (0,2) -- (5,2);
651            \draw[-] (0,3) -- (5,3);
652            \draw[-] (0,0) -- (0,4);
653            \draw[-] (1,0) -- (1,4);           
654            \draw[-] (2,0) -- (2,4);             
655            \draw[-] (3,0) -- (3,4);
656            \draw[-] (4,0) -- (4,4);           
657            \draw[-] (5,4) -- (5,0);
658            \draw[-] (0,4) -- (5,4);
659           
660            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd1) at (1.75,1.3) {};
661            \node[scale=0.8] at (rd1) {1};
662         
663            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd2) at (1.2,2.3) {};
664            \node[scale=0.8] at (rd2) {2};
665            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd3) at (2.3,2.3) {};
666            \node[scale=0.8] at (rd3) {3};
667            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd4) at (3.25,1.21) {};
668            \node[scale=0.8] at (rd4) {4};     
669            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd5) at (3.2,2.7) {};
670            \node[scale=0.8] at (rd5) {5};
671            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd6) at (3.25,1.7) {};
672            \node[scale=0.8] at (rd6) {6};   
673            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd7) at (1.25,1.6) {};
674            \node[scale=0.8] at (rd7) {7};
675            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd8) at (3.7,0.5) {};
676            \node[scale=0.8] at (rd8) {8};     
677            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd9) at (3.77,1.8) {};
678            \node[scale=0.8] at (rd9) {9};
679            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd10) at (2.6,1.3) {};
680            \node[scale=0.8] at (rd10) {10};
681            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd11) at (2.7,0.7) {};
682            \node[scale=0.8] at (rd11) {11};
683            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd12) at (0.21,1.3) {};
684            \node[scale=0.8] at (rd12) {12};
685            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd13) at (0.3,2.5) {};
686            \node[scale=0.8] at (rd13) {13};
687            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd14) at (1.75,2.5) {};
688            \node[scale=0.8] at (rd14) {14};     
689            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd15) at (2.3,1.7) {};
690            \node[scale=0.8] at (rd15) {15};
691            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd16) at (2.4,2.8) {};
692            \node[scale=0.8] at (rd16) {16};   
693            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd17) at (4.23,0.7) {};
694            \node[scale=0.8] at (rd17) {17};
695            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd18) at (3.77,2.6) {};
696            \node[scale=0.8] at (rd18) {18};     
697            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd19) at (4.23,3.3) {};
698            \node[scale=0.8] at (rd19) {19};
699            \node[circle, draw, thick, fill=red!90, scale=1.1] (rd20) at (3.75,1.23) {};
700            \node[scale=0.8] at (rd20) {20}
701         \end{tikzpicture}
702         };
703   \end{tikzpicture} 
704\end{frame}
705
706% Folie 11
707\begin{frame}[t]
708   \frametitle{Basic Particle Parameters (VI)}
709   \small
710   Example for the beneficial effect of resorting on the consumption of CPU time \texttt{(dt\underline{ }sort\underline{ }particles = 0.0)}:\\
711   \scriptsize \ \\
712   Release of 3.200.000 particles into a convective boundary layer.\\
713   Extract from CPU time measurement file.\\
714   \ \\
715
716   \begin{tabular}{|p{2.5cm}|p{1.3cm}|p{1.3cm}|p{1.3cm}|p{1.3cm}|p{1.3cm}|}
717      \hline
718           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 \%\\
719      \hline
720           total & 50027.225 & 100.0 & 47805.635  & 100.0 & \textcolor{red}{4.4}\\
721      \hline
722           advec\underline{ }particles & 22049.711 & 44.08 & 19926.364  & 41.68  & \textcolor{red}{9.6}\\
723      \hline
724           advec\underline{ }particles\underline{ }advec & 13640.729 & 27.27 & 11424.540  & 23.90  & \textcolor{red}{16.2}\\
725      \hline
726   \end{tabular}
727
728
729\end{frame}
730
731% Folie 12
732\begin{frame}[t]
733   \frametitle{Basic Particle Parameters (VII)}
734   \small
735   \vspace{-2mm}
736   Parameters that define the boundary conditions for particles\\
737   \scriptsize \ \\
738   \uncover<10>{In PALM particles are \textbf{always} reflected at \textbf{vertical walls and roofs of buildings.}}\\
739   \ \\
740
741   \begin{tikzpicture}
742      \definecolor{darkgreen}{rgb}{0.2,0.7,0.2}
743      % Bottom
744      \uncover<2>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
745         (0,0) --
746         (2,1.5) --
747         (7,1.5) --
748         (5,0) -- cycle ;}
749      % Top
750      \uncover<4>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
751         (0,4) --
752         (2,5.5) --
753         (7,5.5) --
754         (5,4) -- cycle ;}
755      % Front
756      \uncover<6>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
757         (0,0) --
758         (0,4) --
759         (5,4) --
760         (5,0) -- cycle ;}
761      % Back
762      \uncover<6>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
763         (2,1.5) --
764         (7,1.5) --
765         (7,5.5) --
766         (2,5.5) -- cycle ;}
767      % Left
768      \uncover<8>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
769         (0,0) --
770         (0,4) --
771         (2,5.5) --
772         (2,1.5) -- cycle ;}
773      % Right
774      \uncover<8>{\draw[fill=darkgreen,draw=darkgreen,opacity=.85]
775         (5,0) --
776         (5,4) --
777         (7,5.5) --
778         (7,1.5) -- cycle ;}
779         
780      % Draw Box 
781      \draw[-] (0,0) -- (5,0);
782      \draw[-] (0,0) -- (0,4);
783      \draw[-] (5,4) -- (5,0);
784      \draw[-] (0,4) -- (5,4);
785     
786      \draw[-] (2,1.5) -- (7,1.5);
787      \draw[-] (2,1.5) -- (2,5.5);
788      \draw[-] (7,5.5) -- (7,1.5);
789      \draw[-] (2,5.5) -- (7,5.5);
790     
791      \draw[-] (0,0) -- (2,1.5);
792      \draw[-] (5,0) -- (7,1.5);
793      \draw[-] (5,4) -- (7,5.5);
794      \draw[-] (0,4) -- (2,5.5);
795     
796      \node at (4,5) {\small Total model domain};
797     
798      % Labels
799      \uncover<2->{\node at (2.7,0.15) {\scriptsize \texttt{bc\underline{ }par\underline{ }b = 'reflect', 'absorb'}};} 
800      \uncover<4->{\node at (3.0,4.25) {\scriptsize \texttt{bc\underline{ }par\underline{ }t = 'absorb', 'reflect'}};}       
801      \uncover<6->{\node at (3.25,2.15) {\scriptsize \texttt{bc\underline{ }par\underline{ }ns = 'cyclic', 'reflect', 'absorb'}};}     
802      \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'}};}           
803
804               
805      % Draw coordinate system
806      \node at (9,2) [scale=1.0] {%
807      \begin{tikzpicture}
808         \draw[->] (0,0) -- (1,0);
809         \draw[->] (0,0) -- (0,1);
810         \draw[->] (0,0) -- (0.5,0.5);
811         \node at (-0.2,0.9) {z};
812         \node at (0.9,-0.2) {x};
813         \node at (0.65,0.3) {y};
814      \end{tikzpicture}
815      };
816     
817   \end{tikzpicture}
818   
819\end{frame}
820
821% Folie 13
822\begin{frame}
823   \frametitle{Basic Particle Parameters (VIII)}
824   \small
825   Parameters that steer the output of particle data
826   \begin{itemize}
827      \item There are two output files containing particle data:
828      \begin{itemize}
829         \item \texttt{DATA\underline{ }1D\underline{ }PTS\underline{ }NETCDF}:
830         \hspace{0.5em} contains particle time series, output\\ 
831         \hspace{11.0em}interval is controlled by parameter\\ 
832         \hspace{11.0em}\texttt{dt\underline{ }dopts}, one file for the total\\ 
833         \hspace{11.0em}domain, e.g. time series of the total\\
834         \hspace{11.0em}number of particles, mean particle\\
835         \hspace{11.0em}velocity, mean subgrid scale part of\\
836         \hspace{11.0em}the particle velocity, mean particle\\
837         \hspace{11.0em}location etc.
838         \vspace{1mm}
839         \item \texttt{DATA\underline{ }PRT\underline{ }NETCDF}:
840         \hspace{2.5em}contains \textbf{all} particle data (see slide\\
841         \hspace{11.0em}The Data Type Used for Particles),\\
842         \hspace{11.0em}output is controlled by\\
843         \hspace{11.0em}\texttt{dt\underline{ }write\underline{ }particle\underline{ }data},\\
844         \hspace{11.0em}one file per subdomain/PE
845      \end{itemize}
846   \end{itemize}
847\end{frame}
848
849% Folie 14
850\begin{frame}
851   \frametitle{An Example of a Particle NAMELIST}
852   \includegraphics[scale=0.3]{particle_model_figures/namelist.png}
853   \begin{itemize}
854      \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.)
855   \end{itemize}
856\end{frame}
857
858% Folie 15
859\begin{frame}[t]
860   \frametitle{Theory of the Lagrangian Particle Model (I)}
861   \textbf{Advection of Passive particles}\\
862   \small
863   \vspace{1mm}
864   The position of a particle is found by integrating $ \dfrac{d \vec{X}_{\text{particle}}}{dt} = \vec{V}_{\text{particle}}$\\
865   \vspace{2mm}
866   \onslide<2->Transferring the LES concept ...
867   \includegraphics[scale=0.1]{particle_model_figures/basic_particle_parameters_5.png}\\
868   \vspace{-2mm}
869   \scriptsize \hspace{2em}total energy\hspace{2.25em}=\hspace{3em}resolved part\hspace{2.5em}+\hspace{3em}modelled part\\
870   \vspace{1mm}
871   \small ... to the embedded particle model leads to: $\vec{V}_{\text{particle}} = \vec{V}_{\text{res}} (+ \vec{V}_{\text{sub}})$\\
872   \vspace{2mm}
873   \onslide<3->$\vec{V}_{\text{res}}:$\\ 
874   \begin{tikzpicture}[remember picture, overlay]
875      \node [shift={(1.7 cm,0.6cm)}]  at (current page.south west)
876         {%   
877         \begin{tikzpicture}[scale=0.3,remember picture, overlay]
878            \draw[-] (0,0) -- (5,0);
879            \draw[-] (0,0) -- (0,4);
880            \draw[-] (5,4) -- (5,0);
881            \draw[-] (0,4) -- (5,4);
882            \draw[-] (2,1.5) -- (7,1.5);
883            \draw[-] (2,1.5) -- (2,5.5);
884            \draw[-] (7,5.5) -- (7,1.5);
885            \draw[-] (2,5.5) -- (7,5.5);
886            \draw[-] (0,0) -- (2,1.5);
887            \draw[-] (5,0) -- (7,1.5);
888            \draw[-] (5,4) -- (7,5.5);
889            \draw[-] (0,4) -- (2,5.5);
890     
891            \node[circle, fill=blue, scale=0.5] at (0,0) {};
892            \node[circle, fill=blue, scale=0.5] at (5,0) {};
893            \node[circle, fill=blue, scale=0.5] at (0,4) {};
894            \node[circle, fill=blue, scale=0.5] at (5,4) {};
895            \node[circle, fill=blue, scale=0.5] at (2,1.5) {};
896            \node[circle, fill=blue, scale=0.5] at (7,1.5) {};
897            \node[circle, fill=blue, scale=0.5] at (7,5.5) {};
898            \node[circle, fill=blue, scale=0.5] at (2,5.5) {};
899     
900            \node[circle, fill=red, scale=0.5] at (2.5,1.1) {};
901
902            \draw[->, ultra thick, color=red] (7.4,0.7) -- (2.9,1.1);
903            \node at (9.0,0.1) {\scriptsize \textcolor{red}{particle location}};
904     
905            \draw[->, ultra thick] (8,2.5) -- (12,2.5);
906         \end{tikzpicture}
907         };
908      \node [shift={(5.8 cm,0.6cm)}]  at (current page.south west)
909         {%   
910         \begin{tikzpicture}[scale=0.3,remember picture, overlay]
911            \definecolor{darkgreen}{rgb}{0.2,0.7,0.2}
912            \draw[-] (0,0) -- (5,0);
913            \draw[-] (0,4) -- (5,4);
914            \draw[-] (2,1.5) -- (7,1.5);
915            \draw[-] (2,5.5) -- (7,5.5);
916            \draw[-] (0,0) -- (2,1.5);
917            \draw[-] (5,0) -- (7,1.5);
918            \draw[-] (5,4) -- (7,5.5);
919            \draw[-] (0,4) -- (2,5.5);
920     
921            \node[circle, fill=blue, scale=0.5] at (0,0) {};
922            \node[circle, fill=blue, scale=0.5] at (5,0) {};
923            \node[circle, fill=blue, scale=0.5] at (0,4) {};
924            \node[circle, fill=blue, scale=0.5] at (5,4) {};
925            \node[circle, fill=blue, scale=0.5] at (2,1.5) {};
926            \node[circle, fill=blue, scale=0.5] at (7,1.5) {};
927            \node[circle, fill=blue, scale=0.5] at (7,5.5) {};
928            \node[circle, fill=blue, scale=0.5] at (2,5.5) {};
929           
930            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,0.6) {};       
931            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,4.6) {};         
932            \draw[->, ultra thick] (8,2.5) -- (12,2.5);
933         \end{tikzpicture}
934         };
935      \node [shift={(9 cm,0.6cm)}]  at (current page.south west)
936         {%   
937         \begin{tikzpicture}[scale=0.3,remember picture, overlay]
938            \definecolor{darkgreen}{rgb}{0.2,0.7,0.2}
939           
940            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,0.6) {};       
941            \node[circle, fill=red, scale=0.5] at (2.5,1.1) {};
942            \node[circle, draw, color=darkgreen, ultra thick, scale=0.5] at (2.5,4.6) {};         
943         \end{tikzpicture}
944         };
945      \end{tikzpicture}
946\end{frame}
947
948% Folie 16
949\begin{frame}[t]
950   \frametitle{Theory of the Lagrangian Particle Model (II)}
951   \scriptsize \textbf{A: Passive particles}\\
952   \ \\
953   \uncover<10->{\normalsize \textbf{\underline{Calculation of the subgrid part of the particle velocity $\vec{V}_{\text{sub}}$:}}}
954   \footnotesize
955   \begin{itemize}
956      \item<3-> Application of the method of Weil et al. (2004)
957      \item<2-> \uncover<4->{they derived an adaptation of Thomson's model (1987)}\\
958      \vspace{1mm}
959      \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}\\
960      \vspace{1mm}
961      \uncover<5->{to the grid-volume level, i.e.:}
962      \item<6-> Ensemble-mean velocity replaced by the LES resolved velocity
963      \item<7-> Lagrangian stochastic model describes the subgrid scale random velocity fluctuation about the resolved velocity
964      \item<8-> The subgrid scale velocities are specified by a Gaussian probability density function based on the subgrid scale stress tensor and its inverse
965      \item<9-> The ensemble mean dissipation rate can be replaced by the local dissipation rate     
966   \end{itemize}
967\end{frame}
968
969% Folie 17
970\begin{frame}[t]
971   \frametitle{Theory of the Lagrangian Particle Model (III)}
972   \scriptsize \textbf{A: Passive particles}\\
973   \ \\
974   \normalsize \textbf{\underline{Weil's formula for the subgrid part of the particle velocity:}}
975   \footnotesize \\
976   \vspace{2mm}
977   Assumption: subgrid scale turbulence locally isotropic\\
978   \vspace{6mm}
979   $dV_{\text{sub}_i} = - \dfrac{3 f_s C_0 \varepsilon}{4} \dfrac{V_{\text{sub}_i}}{e_s} dt + \dfrac{1}{3} \left( \dfrac{\partial e_s}{\partial x_i} + \dfrac{3}{2 e_s} \dfrac{d e_s}{dt} V_{\text{sub}_i}\right) dt + \sqrt{f_s C_0 \varepsilon}\, d\xi_i$\\
980   \vspace{2mm}
981   $f_s = \dfrac{\langle 2 e_s / 3 \rangle}{\langle 2 e_s / 3 \rangle + \langle \left( \sigma^2_{\text{res}U} + \sigma^2_{\text{res}V} + \sigma^2_{\text{res}W} \right) /3 \rangle}$\\
982   \vspace{6mm}
983   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\\
984\end{frame}
985
986% Folie 18
987\begin{frame}[t]
988   \frametitle{Theory of the Lagrangian Particle Model (IV)}
989   \scriptsize \textbf{A: Passive particles}\\
990   \ \\
991   \normalsize \textbf{\underline{Particle time step in case of \texttt{use\underline{ }sgs\underline{ }for\underline{ }particles = .TRUE.}:}}
992   \footnotesize \\
993   \vspace{2mm}
994   limited by the Lagrangian time scale $T_L$ \qquad $dt=0.025 T_L$\\
995   \vspace{3mm}
996   subsequent particle time steps: velocities correlated, accelerations not correlated\\
997   \vspace{3mm}
998   Lagrangian autocorrelation function:\\
999   \begin{tikzpicture}[domain=0:4]
1000      \draw[->] (0,0) -- (4.5,0);
1001      \draw[->] (0,0) -- (0,2);
1002      \node at (4.5,-0.3) {$\tau$};
1003      \node at (-0.5,1.8) {$R_L(\tau)$};
1004      \draw[thick, domain=0:4] plot (\x,{1.7*exp(-1.6*\x)+0.05});
1005   \end{tikzpicture}\\
1006   $R_L(\tau) = \dfrac{W(t) W(t + \tau)}{\sigma^2_w} = exp\left( - \dfrac{\tau}{T_L} \right) \hspace{10mm} T_L = 4 e_s / (3 f_s C_0 \varepsilon)$\\
1007   \ \\
1008   Particle time step can be smaller than LES time step!
1009\end{frame}
1010
1011% Folie 19
1012\begin{frame}[t]
1013   \frametitle{Theory of the Lagrangian Particle Model (V)}
1014   \scriptsize \textbf{B: Non-passive particles (e.g. cloud droplets) }\\
1015   \ \\
1016   \footnotesize
1017   $\rightarrow$ advection of particles by the non-linear drag law following Clift et al., 1978\\
1018   \vspace{4mm}
1019   \onslide<2->$\dfrac{dV_i}{dt} = \dfrac{1}{\tau_p} (u_i - V_i -\delta_{i3}w_s) \rightarrow V_i(t) = V_i(0) e^{-\Delta t / \tau_p} + (u_i -w_s \delta_{i3}) \left( 1 - e^{-\Delta t / \tau_p} \right)$\\
1020      \vspace{2mm}
1021   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} $\beta = \dfrac{\rho_p}{\rho_f}$\\
1022   \vspace{5mm}
1023   \onslide<1->
1024   \begin{tabular}{llll}
1025           $C_D$ & = drag coefficient           & $w_s$    & = terminal velocity\\
1026           $g$   & = gravitational acceleration & $\beta$  & = density coefficient\\
1027           Re    & = Reynolds number            & $\rho_p$ & = density of the particle\\
1028           $u_i$ & = velocity of the fluid      & $\rho_f$ & = density of the fluid\\
1029           $V_i$ & = particle velocity          & $\tau_p$ & = response time with respect to inertia\\
1030   \end{tabular}
1031\end{frame}
1032
1033
1034% Folie 20
1035\begin{frame}
1036   \frametitle{Flow Chart of Particle Code (I)}
1037   \footnotesize
1038   \begin{tikzpicture}[scale=0.8, transform shape]
1039      % Define colours
1040      \tikzstyle{gelb1} = [draw, fill=yellow!60, text width=7em, text centered, minimum height=1.6em]
1041      \tikzstyle{orange} = [draw, fill=orange!60, text width=7em, text centered]
1042     
1043      % Define coordinates and draw nodes     
1044      \node[gelb1, text width=5em] (PALM) at (0,0.1) {PALM};
1045
1046      \coordinate (A) at (0,-0.7);
1047
1048      \node[gelb1, right=0.6cm of A] (init3d) {init\underline{ }3d\underline{ }model};
1049     
1050      \coordinate[below=0.4cm of init3d] (B) ;
1051      \coordinate[below=1.0cm of init3d] (C) ;       
1052      \coordinate[below=1.6cm of init3d] (D) ;       
1053      \coordinate[below=2.2cm of init3d] (E) ;       
1054      \coordinate[below=2.8cm of init3d] (F) ;       
1055      \coordinate[below=4.2cm of init3d] (G) ;     
1056      \coordinate[below=4.8cm of init3d] (H) ;     
1057      \coordinate[below=7cm of init3d] (I) ;   
1058      \coordinate (J) at (0,-8.6);
1059           
1060      \node[gelb1, right=0.5cm of B, text width=17em] (init1d) {init\underline{ }1d\underline{ }model (\textit{calls various subroutines})};
1061      \node[gelb1, right=0.5cm of C] (initslope) {init\underline{ }slope};
1062      \node[gelb1, right=0.5cm of D] (disturb) {disturb\underline{ }heatflux};
1063      \node[gelb1, right=0.5cm of E] (initrankine) {init\underline{ }rankine};
1064      \node[gelb1, right=0.0cm of initrankine] {init\underline{ }pt\underline{ }anomaly};
1065      \node[gelb1, right=0.5cm of F] (disturbfield) {disturb\underline{ }field};
1066      \node[gelb1, right=0.0cm of disturbfield] (pres) {pres};
1067      \node[gelb1, right=0.5cm of G] (read3d) {read\underline{ }3d\underline{ }binary};
1068      \node[gelb1, right=0.0cm of read3d] (initdvrp) {init\underline{ }dvrp};
1069      \node[gelb1, right=0.0cm of initdvrp] (initocean) {init\underline{ }ocean};
1070      \node[gelb1, right=0.0cm of initocean] {init\underline{ }cloud\underline{ }physics};           
1071      \node[orange, right=0.5cm of H] (initparticles) {init\underline{ }particles};     
1072      \node[gelb1, right=0.5cm of I] (initadvec) {init\underline{ }advec};     
1073      \node[gelb1, right=0.0cm of initadvec] (userinit) {user\underline{ }init};
1074      \node[gelb1, right=0.6cm of J] (dataoutput2d) {data\underline{ }output\underline{ }2d};     
1075      \node[gelb1, right=0.0cm of dataoutput2d] {data\underline{ }output\underline{ }3d};         
1076
1077      \coordinate[below=0.15cm of pres] (K);
1078      \coordinate[right=0.2cm of K] (L);
1079      \coordinate[right=2cm of L] (M);
1080      \coordinate[right=2cm of M] (N);
1081           
1082      \node[gelb1, below=0.1cm of L, text width=4em] (poisfft) {poisfft};
1083      \node[gelb1, below=0.1cm of M, text width=4em] (sor) {sor};
1084      \node[gelb1, below=0.1cm of N, text width=4em] (poismg) {poismg};
1085     
1086      \coordinate[below=0.1cm of initparticles] (O);
1087      \coordinate[below=0.6cm of O] (P);
1088      \coordinate[below=0.6cm of P] (Q);
1089     
1090      \node[orange, right=1.5cm of O] (userinitparticles) {user\underline{ }init\underline{ }particles};
1091      \node[orange, right=1.5cm of P] (sortparticles) {sort\underline{ }particles};
1092      \node[orange, right=1.5cm of Q] (dataoutputdvrp) {data\underline{ }output\underline{ }dvrp};
1093     
1094      \coordinate[right=1.5cm of dataoutputdvrp] (R);
1095
1096      \node[orange, below=0.3cm of R] (userdvrp) {user\underline{ }dvrp\underline{ }coltab};
1097   
1098      % Draw lines 
1099      \draw[dotted, thick] (PALM) -- (0,-0.5);
1100      \draw[-, thick] (0,-0.5) -- (0,-8.7);
1101      \draw[dotted, thick] (0,-8.7) -- (0,-9.0);     
1102      \draw[-, thick] (init3d.west) -- (A) ;
1103      \draw[-, thick] (init3d.south) -- (I) ;
1104      \draw[dashed, thick] (B) -- (init1d.west);
1105      \draw[dashed, thick] (C) -- (initslope.west);
1106      \draw[dashed, thick] (D) -- (disturb.west);
1107      \draw[dashed, thick] (E) -- (initrankine.west);
1108      \draw[dashed, thick] (F) -- (disturbfield.west);
1109      \draw[dashed, thick] (G) -- (read3d.west);     
1110      \draw[-, thick] (H) -- (initparticles.west);     
1111      \draw[-, thick] (I) -- (initadvec.west);         
1112      \draw[dashed, thick] (J) -- (dataoutput2d);     
1113      \draw[-, thick] (pres.south) -- (K);
1114      \draw[-, thick] (K) -- (N);
1115      \draw[-, thick] (L) -- (poisfft.north);
1116      \draw[-, thick] (M) -- (sor.north);     
1117      \draw[-, thick] (N) -- (poismg.north);       
1118      \draw[-, thick] (initparticles.south) -- (P);
1119      \draw[dashed, thick] (P) -- (Q);
1120      \draw[-, thick] (O) -- (userinitparticles.west);
1121      \draw[-, thick] (P) -- (sortparticles.west);
1122      \draw[dashed, thick] (Q) -- (dataoutputdvrp.west);           
1123      \draw[-, thick] (dataoutputdvrp.east) -- (R);
1124      \draw[-, thick] (R) -- (userdvrp.north);
1125     
1126   \end{tikzpicture}
1127   
1128   
1129\end{frame}
1130
1131% Folie 21
1132\begin{frame}
1133   \frametitle{Flow Chart of Particle Code (II)}
1134   \footnotesize
1135   \begin{tikzpicture}[scale=0.8, transform shape]
1136      % Define colours
1137      \tikzstyle{gelb1} = [draw, fill=yellow!60, text width=7em, text centered, minimum height=1.6em]
1138      \tikzstyle{orange} = [draw, fill=orange!60, text width=7em, text centered]
1139     
1140      % Define coordinates and draw nodes
1141      \coordinate (A) at (0,-0.7);
1142
1143      \node[gelb1, right=0.6cm of A] (timeintegration) {time\underline{ }integration};
1144     
1145      \coordinate[below=0.3 of timeintegration] (B);
1146      \coordinate[below=0.9 of timeintegration] (C);
1147     
1148      \node[gelb1, right=0.6cm of B] (timestep) {timestep};
1149      \node[gelb1, right=0.6cm of C] (runcontrol) {run\underline{ }control};
1150     
1151      \coordinate[below=0.2cm of runcontrol] (D);
1152     
1153      \node[gelb1, right=1.5cm of D] (flowstat) {flow\underline{ }statistics};
1154     
1155      \coordinate[below=1.8cm of timeintegration] (E);
1156     
1157      \node[gelb1, right=0.6cm of E] (surface) {surface\underline{ }coupler};
1158     
1159      \coordinate[below=2.4cm of timeintegration] (F);
1160       
1161      \node[gelb1, right=0.6cm of F, text width=13em] (useractions) {user\underline{ }actions (\textit{before\underline{ }timestep})};   
1162 
1163       \coordinate[below=3.0cm of timeintegration] (G);
1164       
1165      \node[gelb1, right=0.6cm of G, text width=11em] (timestepscheme) {timestep\underline{ }scheme\underline{ }steering};       
1166     
1167      \coordinate[below=3.5cm of timeintegration] (H);
1168      \coordinate[right=2cm of H] (I);
1169      \coordinate[right=3.5cm of I] (J);
1170     
1171      \node[draw, text width=22em,minimum height=4.5em,fill=black!15] (progframe) at (5.75,-5.3) {};
1172      \node[draw, text width= 9.5em, right=0.5cm of progframe] {For details, see PALM Flow Chart (V).};
1173      \node[gelb1, below=0.3cm of I, text width=9em] (prog) {prognostic\underline{ }equations};     
1174      \node[gelb1, below=0.3cm of J, text width=10.5em] (progfast) {prognostic\underline{ }equations\underline{ }fast}
1175      \node[gelb1, below=0.1cm of progfast, text width=10.5em] (progvec) {prognostic\underline{ }equations\underline{ }vec};       
1176      \node[draw, fill=red, text width=4em] at (8.2,-4) {\textcolor{white}{standard advection}};
1177     
1178      \coordinate[below=5.5cm of timeintegration] (K);
1179     
1180      \node[orange, right=0.6cm of K] (advecparticles) {advec\underline{ }particles};             
1181     
1182      \coordinate[below=0.2cm of advecparticles] (L);
1183     
1184      \node[orange, right=1.5cm of L, text width=13em] (userparticlesatt) {user\underline{ }particle\underline{ }attributes + more};
1185     
1186      \coordinate[below=6.6cm of timeintegration] (M);
1187     
1188      \node[orange, right=0.6cm of M, text width=10em] (interaction) {interaction\underline{ }droplets\underline{ }ptq};     
1189
1190      \coordinate[below=7.2cm of timeintegration] (N);
1191     
1192      \node[gelb1, right=0.6cm of N] (asselin) {asselin\underline{ }filter};     
1193     
1194      \coordinate[below=7.8cm of timeintegration] (O);
1195     
1196      \node[gelb1, right=0.6cm of O] (boundary) {boundary\underline{ }conds};       
1197      \node[gelb1, right=0.0cm of boundary] {swap\underline{ }timelevel}
1198           
1199      \coordinate[below=8.4cm of timeintegration] (P);     
1200     
1201      \node[gelb1, right=0.6cm of P] (inflow) {inflow\underline{ }turbulence};
1202      \node[gelb1, right=0.0cm of inflow] {disturb\underline{ }field};
1203                                                     
1204      % Draw lines 
1205      \draw[dotted, thick] (0,-0.3) -- (0,-0.7);
1206      \draw[-, thick] (0,-0.7) -- (0,-7.7);
1207      \draw[dotted, thick] (0,-7.7) -- (0,-9.0);     
1208      \draw[-, thick] (A) -- (timeintegration);
1209      \draw[-, thick] (B) -- (timestep);
1210      \draw[-, thick] (C) -- (runcontrol);
1211      \draw[-, thick] (runcontrol.south) -- (D);
1212      \draw[-, thick] (D) -- (flowstat);
1213      \draw[dashed, thick] (E) -- (surface);
1214      \draw[-, thick] (F) -- (useractions);     
1215      \draw[-, thick] (G) -- (timestepscheme);
1216      \draw[-, thick] (H) -- (I);
1217      \draw[-, thick] (I) -- (prog.north);
1218      \draw[-, thick, color=red] (I) -- (J);       
1219      \draw[->, thick, color=red] (J) -- (progfast.north);
1220      \draw[dashed, thick] (K) -- (advecparticles);           
1221      \draw[-, thick] (advecparticles.south) -- (L);           
1222      \draw[-, thick] (L) -- (userparticlesatt.west);       
1223      \draw[dashed, thick] (M) -- (interaction.west); 
1224      \draw[dashed, thick] (N) -- (asselin.west);       
1225      \draw[-, thick] (O) -- (boundary.west); 
1226      \draw[dashed, thick] (P) -- (inflow.west);             
1227      \draw[-, thick] (timeintegration.south) -- (O); 
1228      \draw[dashed, thick] (O) -- (P); 
1229     
1230   \end{tikzpicture}   
1231   
1232\end{frame}
1233
1234
1235% Folie 22
1236\begin{frame}
1237   \frametitle{Detailed Flow Chart of \texttt{advec\underline{ }particles} (I)}
1238   \scriptsize
1239   \begin{tikzpicture}[scale=0.87, transform shape]
1240      \node (0) at (0,0) {};
1241      \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/})};}
1242      \uncover<3->{\node[draw, right=0.0cm of 0, yshift=-0.9cm] {calculate exponential terms for particles groups with inertia};}
1243      \uncover<4->{\node[draw, right=0.0cm of 0, yshift=-1.5cm] {particle growth by condensation/evaporation and collision};}
1244      \uncover<5->{\node[draw, right=0.0cm of 0, yshift=-2.1cm] {If SGS-velocities are used: calculate gradients of TKE};}
1245      \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})};}
1246      \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};}
1247      \uncover<8->{\node[draw, right=0.5cm of 0, yshift=-4.8cm] {calculate particle reflection from walls (subroutine \texttt{particle\underline{ }boundary\underline{ }conds})};}
1248      \uncover<9->{\node[draw, right=0.5cm of 0, yshift=-5.4cm] {user defined actions (subroutine \texttt{user\underline{ }advec\underline{ }particles})};}     
1249      \uncover<10->{\node[draw, right=0.5cm of 0, yshift=-6.0cm] {if necessary, release a new set of particles};}
1250      \uncover<11->{\node[draw, right=0.5cm of 0, yshift=-6.6cm] {particle exchange between the subdomains};}   
1251      \uncover<12->{\node[draw, right=0.5cm of 0, yshift=-7.2cm] {boundary conditions at bottom and top};}
1252      \uncover<13->{\node[draw, right=0.5cm of 0, yshift=-7.8cm] {delete, pack, and sort particles};}   
1253   \end{tikzpicture}
1254\end{frame}
1255
1256% Folie 23
1257\begin{frame}
1258   \frametitle{Detailed Flow Chart of \texttt{advec\underline{ }particles} (II)}
1259   \scriptsize
1260   \begin{tikzpicture}[auto, node distance=0]
1261      \node (0) at (0,0) {};
1262      \node[draw, right=0.0cm of 0] {In case of cloud droplets: calculate the liquid water content};
1263      \uncover<2->{\node[draw, right=0.0cm of 0, yshift=-0.6cm] {user defined setting of particle attributes (subroutine \texttt{user\underline{ }particle\underline{ }attributes})};}
1264      \uncover<3->{\node[draw, right=0.0cm of 0, yshift=-1.2cm] {if necessary, add actual positions to the particle tails};}
1265      \uncover<4->{\node[draw, right=0.0cm of 0, yshift=-1.8cm] {write particle statistics on file \texttt{PARTICLE\underline{ }INFOS} (ASCII format)}}   
1266   \end{tikzpicture}
1267   \vspace{5mm}
1268   \small
1269   \begin{itemize}
1270      \item<5-> For a better modular structure, subroutine advec\underline{ }particles will be split into several subroutines in one of the next PALM releases.
1271   \end{itemize}
1272\end{frame}
1273
1274% Folie 24
1275\begin{frame}
1276   \frametitle{The Data Type Used for Particles}
1277   \small
1278   \begin{itemize}
1279      \item Particle data are stored in a FORTRAN derived data type:
1280   \end{itemize}
1281   \includegraphics[scale=0.3]{particle_model_figures/data_type.png}
1282\end{frame}
1283
1284% Folie 25
1285\begin{frame}
1286   \frametitle{How to Read netCDF Particle Data from an External Program}
1287   \footnotesize
1288   \begin{itemize}
1289      \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}
1290       \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!\\
1291       \vspace{1mm}
1292       Both informations can only be found on file PARTICLE\underline{ }DATA/.\\
1293       \vspace{1mm}
1294       For the format of this file (one per PE, i.e. filenames \underline{ }0000, \underline{ }0001, etc.) see beginning of subroutine advec\underline{ }particles.
1295   \end{itemize}
1296   \onslide<3->\hspace{4mm}\includegraphics[scale=0.27]{particle_model_figures/particle_data.png}
1297\end{frame}
1298
1299% Folie 26
1300\begin{frame}
1301   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (I)}
1302   \footnotesize
1303   \textbf{What is a footprint?}
1304   \begin{itemize}
1305      \item field of view of a micrometeorological measurement
1306   \end{itemize}
1307   \onslide<2->
1308   \textbf{What is the motivation for footprint modelling?}
1309   \begin{itemize}
1310      \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
1311   \end{itemize}
1312   \onslide<3->
1313   \textbf{How is it done?}
1314   \begin{itemize}
1315      \item particle trajectories are calculated in LES using embedded Lagrangian Particle Model
1316      \item once a particle intersects with chosen measuring height, footprint relevant data is output
1317      \item footprints are calculated in postprocessing
1318   \end{itemize}
1319   \onslide<4->
1320   \textbf{What to keep in mind?}
1321   \begin{itemize}
1322      \item including subgridscale particle velocities necessary, when calculating footprints close to the surface, where subgridscale contribution\\to turbulent kinetic energy is relatively large
1323   \end{itemize}
1324\end{frame}
1325
1326% Folie 27
1327\begin{frame}
1328   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (II)}
1329   \footnotesize
1330   \begin{center}
1331      \includegraphics[scale=0.4]{particle_model_figures/footprint2.png}
1332   \end{center}
1333   \vspace{-6mm}
1334   \begin{flushright}
1335      after Steinfeld, 2009
1336   \end{flushright}
1337\end{frame}
1338
1339% Folie 28
1340\begin{frame}
1341   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (III)}
1342   \footnotesize
1343   \textbf{Setup} (according to Steinfeld et al., 2008)
1344   \includegraphics[scale=0.285]{particle_model_figures/footprint3_1.png} \hspace{2mm}
1345   \includegraphics[scale=0.5]{particle_model_figures/footprint3_2.png}
1346   \begin{itemize}
1347      \item particles are released every 2min over a period of 30min at z=70m in the total model domain ($\rightarrow$ 7 * $10^6$ particles)
1348      \item particles are measured at z=72.5m, 77.5m, 100.0m
1349   \end{itemize}
1350\end{frame}
1351
1352% Folie 29
1353\begin{frame}
1354   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (IV)}
1355   \footnotesize
1356   Extract from the corresponding parameter file:
1357   \includegraphics[scale=0.285]{particle_model_figures/footprint4.png}
1358\end{frame}
1359
1360% Folie 30
1361\begin{frame}
1362   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (V)}
1363   \footnotesize
1364   Additionally required user-defined code (continued):
1365   \begin{enumerate}
1366      \scriptsize
1367      \setcounter{enumi}{0}
1368      \item     Open files (one per PE and measuring height) for the additional output of footprint relevant particle data in \texttt{user\underline{ }init}
1369   \end{enumerate}
1370   \includegraphics[scale=0.27]{particle_model_figures/footprint5_1.png}
1371   \begin{enumerate}
1372      \scriptsize
1373      \setcounter{enumi}{1}
1374      \item Create directory into which the files containing the particle data shall be moved to and move the files (in .mrun.config)
1375   \end{enumerate}
1376   \includegraphics[scale=0.27]{particle_model_figures/footprint5_2.png}
1377\end{frame}
1378
1379% Folie 31
1380\begin{frame}
1381   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (VI)}
1382   \footnotesize
1383   Additionally required user-defined code (continued):
1384   \begin{enumerate}
1385      \scriptsize
1386      \setcounter{enumi}{2}
1387      \item Output of footprint relevant data in \texttt{user\underline{ }advec\underline{ }particles} (checking if particle has crossed measuring height)
1388   \end{enumerate}
1389   \includegraphics[scale=0.285]{particle_model_figures/footprint6.png}
1390\end{frame}
1391
1392% Folie 32
1393\begin{frame}
1394   \frametitle{Application example: Footprint modelling above a homogeneously heated surface (VII)}
1395   \includegraphics[scale=0.3]{particle_model_figures/example1.png}
1396   \includegraphics[scale=0.35]{particle_model_figures/example2.png}\\
1397   \begin{itemize}
1398      \item sensor position at x = 0m
1399   \end{itemize}
1400\end{frame}
1401
1402% Folie 33
1403\begin{frame}
1404   \frametitle{Using Particles as Cloud Droplets}
1405   \begin{itemize}
1406      \item<1-> This feature is switched on by setting the initial parameter cloud\underline{ }droplets = \textit{.TRUE.}.
1407      \item<2-> In this case, the change in particle radius by condensation/evaporation and collision is calculated for every timestep.
1408      \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.
1409   \end{itemize}
1410\end{frame}
1411
1412% Folie 34
1413\begin{frame}
1414   \frametitle{General Warning}
1415   \begin{itemize}
1416      \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.
1417   \end{itemize}
1418\end{frame}
1419
1420\end{document}
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