From 90fa82533991c68396e5932a85cbaeec200adc60 Mon Sep 17 00:00:00 2001 From: Adrian Kummerlaender Date: Wed, 6 Feb 2019 14:16:29 +0100 Subject: Add cylinder2d comparison plots --- content.tex | 20 +- img/cylinder2d_deltap_comparison.tikz | 39 + img/cylinder2d_drag_comparison.tikz | 39 + img/cylinder2d_lift_comparison.tikz | 39 + ...imized_refinement_n5_re100_drag_lift_deltap.csv | 1716 ++++++++++++++++++++ ...nder2d_unrefined_n12_re100_drag_lift_deltap.csv | 1609 ++++++++++++++++++ 6 files changed, 3461 insertions(+), 1 deletion(-) create mode 100644 img/cylinder2d_deltap_comparison.tikz create mode 100644 img/cylinder2d_drag_comparison.tikz create mode 100644 img/cylinder2d_lift_comparison.tikz create mode 100644 img/data/cylinder2d_optimized_refinement_n5_re100_drag_lift_deltap.csv create mode 100644 img/data/cylinder2d_unrefined_n12_re100_drag_lift_deltap.csv 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 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