diff options
| -rw-r--r-- | content.tex | 20 | ||||
| -rw-r--r-- | img/cylinder2d_deltap_comparison.tikz | 39 | ||||
| -rw-r--r-- | img/cylinder2d_drag_comparison.tikz | 39 | ||||
| -rw-r--r-- | img/cylinder2d_lift_comparison.tikz | 39 | ||||
| -rw-r--r-- | img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv | 1716 | ||||
| -rw-r--r-- | img/data/cylinder2d_unrefined_n12_re100_drag_lift_deltap.csv | 1609 |
6 files changed, 3461 insertions, 1 deletions
diff --git a/content.tex b/content.tex index ef1ae00..6152e39 100644 --- a/content.tex +++ b/content.tex @@ -1072,7 +1072,25 @@ Klar zu erkennen ist die in der verfeinerten Variante deutlich bessere Diskretis Bevor wir dazu kommen bemerken wir, dass sich mit dieser flexibleren Verteilung der Knotenfreiheitsgrade hier auch ein, bis jetzt nur in der Einführung erwähnter, Vorteil von Gitterverfeinerung illustriert: Selbst wenn ein Verfeinerungsverfahren bezogen auf den Fehler im Vergleich mit analytischen Lösungen keine Verbesserungen oder sogar leichte Einbußen produziert, kann es doch potenziell eingesetzt werden, um Probleme zu behandeln, welche anderweitig nicht oder nur mit deutlich höherem Speicher- und Rechenaufwand zugänglich wären.
-\subsubsection{Vergleich von Druckdifferenz und Widerstandskraft}
+\subsubsection{Vergleich von Widerstands- und Auftriebskräften}
+
+\begin{figure}[H]
+\centering
+\input{img/cylinder2d_drag_comparison.tikz}
+\caption{Verlauf der Widerstandskraft verglichen mit \cite[Tabelle~4]{SchaeferTurek96}}
+\end{figure}
+
+\begin{figure}[H]
+\centering
+\input{img/cylinder2d_lift_comparison.tikz}
+\caption{Verlauf der Auftriebskraft verglichen mit \cite[Tabelle~4]{SchaeferTurek96}}
+\end{figure}
+
+\begin{figure}[H]
+\centering
+\input{img/cylinder2d_deltap_comparison.tikz}
+\caption{Verlauf der Druckdifferenz verglichen mit \cite[Tabelle~4]{SchaeferTurek96}}
+\end{figure}
\newpage
\section{Fazit}
diff --git a/img/cylinder2d_deltap_comparison.tikz b/img/cylinder2d_deltap_comparison.tikz new file mode 100644 index 0000000..a8662d1 --- /dev/null +++ b/img/cylinder2d_deltap_comparison.tikz @@ -0,0 +1,39 @@ +\begin{tikzpicture} +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv}\refined +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n12_re100_drag_lift_deltap.csv}\uniform + +\begin{axis}[ + scale only axis, + height=8cm, + width=0.9*\textwidth, + legend cell align=left, + legend pos=south east, + grid=both, + domain=0:16, + xmin=0, xmax=16, + xlabel={Simulierte physikalische Zeit in Sekunden}, + ylabel={Druckdifferenz} +] + +\addplot[ + color=blue!50!white, + very thin +] table [ + x expr=\thisrow{time}, y=deltap +] {\uniform}; +\addlegendentry {Uniformes \(N=12\) Gitter}; + +\addplot[ + color=green!70!black, + thick +] table [ + x expr=8*\thisrow{time}, y=deltap +] {\refined}; +\addlegendentry {Problembezogen verfeinertes \(N=5\) Gitter}; + +\addplot[color=black]{2.48}; +\addlegendentry {Gemittelte Referenzlösung \(\Delta P\)}; + +\end{axis} +\end{tikzpicture} + diff --git a/img/cylinder2d_drag_comparison.tikz b/img/cylinder2d_drag_comparison.tikz new file mode 100644 index 0000000..df9c88f --- /dev/null +++ b/img/cylinder2d_drag_comparison.tikz @@ -0,0 +1,39 @@ +\begin{tikzpicture} +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv}\refined +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n12_re100_drag_lift_deltap.csv}\uniform + +\begin{axis}[ + scale only axis, + height=8cm, + width=0.9*\textwidth, + legend cell align=left, + legend pos=south east, + grid=both, + domain=0:16, + xmin=0, xmax=16, + xlabel={Simulierte physikalische Zeit in Sekunden}, + ylabel={Widerstandskraft} +] + +\addplot[ + color=blue!50!white, + very thin +] table [ + x expr=\thisrow{time}, y=drag +] {\uniform}; +\addlegendentry {Uniformes \(N=12\) Gitter}; + +\addplot[ + color=green!70!black, + thick +] table [ + x expr=8*\thisrow{time}, y=drag +] {\refined}; +\addlegendentry {Problembezogen verfeinertes \(N=5\) Gitter}; + +\addplot[color=black]{3.23}; +\addlegendentry {Gemittelte Referenzlösung \(c_\text{Dmax}\)}; + +\end{axis} +\end{tikzpicture} + diff --git a/img/cylinder2d_lift_comparison.tikz b/img/cylinder2d_lift_comparison.tikz new file mode 100644 index 0000000..8bdc295 --- /dev/null +++ b/img/cylinder2d_lift_comparison.tikz @@ -0,0 +1,39 @@ +\begin{tikzpicture} +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv}\refined +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n12_re100_drag_lift_deltap.csv}\uniform + +\begin{axis}[ + scale only axis, + height=8cm, + width=0.9*\textwidth, + legend cell align=left, + legend pos=south west, + grid=both, + domain=0:16, + xmin=0, xmax=16, + xlabel={Simulierte physikalische Zeit in Sekunden}, + ylabel={Auftriebskraft} +] + +\addplot[ + color=blue!50!white, + very thin +] table [ + x expr=\thisrow{time}, y=lift +] {\uniform}; +\addlegendentry {Uniformes \(N=12\) Gitter}; + +\addplot[ + color=green!70!black, + thick +] table [ + x expr=8*\thisrow{time}, y=lift +] {\refined}; +\addlegendentry {Problembezogen verfeinertes \(N=5\) Gitter}; + +\addplot[color=black]{1.0}; +\addlegendentry {Gemittelte Referenzlösung \(c_\text{Lmax}\)}; + +\end{axis} +\end{tikzpicture} + diff --git a/img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv b/img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv new file mode 100644 index 0000000..70d3ba4 --- /dev/null +++ b/img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv @@ -0,0 +1,1716 @@ +time,drag,lift,deltap +0,0,0,0 +0.00116667,0,0,0 +0.00233333,5.15458e-09,-2.0672e-12,5.96883e-09 +0.0035,9.86995e-07,5.73673e-10,7.04313e-07 +0.00466667,7.65869e-06,4.71829e-09,5.00938e-06 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