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| -rw-r--r-- | content.tex | 6 | ||||
| -rw-r--r-- | img/collide_and_stream.tikz | 51 |
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} |