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authorAdrian Kummerlaender2019-03-02 12:36:17 +0100
committerAdrian Kummerlaender2019-03-02 12:36:17 +0100
commite590ffe9fa29d4e9123aa9aaefcbaae3f893616d (patch)
tree7c819e28bee454a452d540d55548602ceaadc2a8
parentf1f69a5501de308e8d2a9e92df606b6b9354ea3b (diff)
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Add streaming figure
-rw-r--r--content.tex6
-rw-r--r--img/collide_and_stream.tikz51
2 files changed, 57 insertions, 0 deletions
diff --git a/content.tex b/content.tex
index 6c450a4..1ac1a3c 100644
--- a/content.tex
+++ b/content.tex
@@ -170,6 +170,12 @@ Strömen der neuen Verteilungen auf die benachbarten Zellen entsprechend der jew
Bemerkenswert ist hierbei, dass der Kollisionsschritt nur lokale Informationen der jeweiligen Zelle benötigt und sich somit sehr gut zur parallelen Verarbeitung eignet.
+\begin{figure}[h]
+\centering
+\input{img/collide_and_stream.tikz}
+\caption{Strömung der im Kollisionsschritt relaxierten Verteilungen}
+\end{figure}
+
\subsubsection{Chapman-Enskog Analyse}
Ziel der beschriebenen Lattice Boltzmann Methode ist die möglichst gute Approximation der schwach-kompressiblen Navier-Stokes Gleichungen auf der Simulationsdomäne.
diff --git a/img/collide_and_stream.tikz b/img/collide_and_stream.tikz
new file mode 100644
index 0000000..232800f
--- /dev/null
+++ b/img/collide_and_stream.tikz
@@ -0,0 +1,51 @@
+\begin{tikzpicture}[
+ scale=1.5,
+ dot/.style={circle,draw=black,inner sep=3pt},
+ center/.style={circle,fill=black,inner sep=4pt},
+ arrow/.style={draw=black,->,>=stealth},
+]
+
+\foreach \x in {0,...,2}
+ \foreach \y in {0,...,2}
+ \ifthenelse{\x=1 \AND \y=1}{
+ \node[center] at (\x,\y){ };
+ }{
+ \node[dot] at (\x,\y){ };
+ };
+
+\foreach \x in {6,...,8}
+ \foreach \y in {0,...,2}
+ \ifthenelse{\x=7 \AND \y=1}{
+ \node[center] at (\x,\y){ };
+ }{
+ \node[dot] at (\x,\y){ };
+ };
+
+\foreach \x in {1}
+ \foreach \y in {1} {
+ \draw[arrow] (\x+0.2,\y+0.2) -- (\x+0.4,\y+0.4){ };
+ \draw[arrow] (\x+0.2,\y) -- (\x+0.35,\y){ };
+ \draw[arrow] (\x+0.2,\y-0.2) -- (\x+0.4,\y-0.4){ };
+ \draw[arrow] (\x,\y-0.2) -- (\x,\y-0.375){ };
+ \draw[arrow] (\x-0.2,\y-0.2) -- (\x-0.4,\y-0.4){ };
+ \draw[arrow] (\x-0.2,\y) -- (\x-0.5,\y){ };
+ \draw[arrow] (\x-0.2,\y+0.2) -- (\x-0.5,\y+0.5){ };
+ \draw[arrow] (\x,\y+0.2) -- (\x,\y+0.4){ };
+ };
+
+\foreach \x in {7}
+ \foreach \y in {1} {
+ \draw[arrow] (\x+1.2,\y+1.2) -- (\x+1.4,\y+1.4){ };
+ \draw[arrow] (\x+1.2,\y) -- (\x+1.35,\y){ };
+ \draw[arrow] (\x+1.2,\y-1.2) -- (\x+1.4,\y-1.4){ };
+ \draw[arrow] (\x,\y-1.2) -- (\x,\y-1.375){ };
+ \draw[arrow] (\x-1.2,\y-1.2) -- (\x-1.4,\y-1.4){ };
+ \draw[arrow] (\x-1.2,\y) -- (\x-1.5,\y){ };
+ \draw[arrow] (\x-1.2,\y+1.2) -- (\x-1.5,\y+1.5){ };
+ \draw[arrow] (\x,\y+1.2) -- (\x,\y+1.4){ };
+ };
+
+\draw[->,line width=0.5mm] (2.6,1) -- (5,1) node[midway,above] {Strömungsschritt};
+\draw (2.6,1) -- (5,1) node[midway,below] {\(t \mapsto t+1\)};
+
+\end{tikzpicture}