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authorAdrian Kummerlaender2019-02-08 14:44:30 +0100
committerAdrian Kummerlaender2019-02-08 14:44:30 +0100
commitfd7d9f860dba72f1bf5bfd9b305d477846536ac6 (patch)
tree5a3d50500f3b1792b4e84c80a0b5ade866bb3703
parent41d13fbfe30c600b6e0d81bd19810f5003793b76 (diff)
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Add cylinder2d error table
-rw-r--r--content.tex29
-rw-r--r--img/cylinder2d_deltap_comparison.tikz1
-rw-r--r--img/cylinder2d_drag_comparison.tikz1
-rw-r--r--img/cylinder2d_lift_comparison.tikz1
-rw-r--r--img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv1602
5 files changed, 1634 insertions, 0 deletions
diff --git a/content.tex b/content.tex
index dc79976..5b9d0aa 100644
--- a/content.tex
+++ b/content.tex
@@ -1131,5 +1131,34 @@ Die folgenden Abbildungen zeichnen demnach den zeitlichen Verlauf der durch das
\newpage
Klar zu erkennen ist, dass die Simulation auf dem verfeinerten Gitter über alle drei Kriterien sowohl die Referenzwerte besser trifft als auch unabhängig davon eine bessere Qualität bezogen auf Fluktuation und Konsistenz in der periodischen Strömungsphase aufweist. Da diese Ergebnisse bei näherungsweise beibehaltener Anzahl von Gitterknoten erzielt wurden -- tatsächlich verwendet das verfeinerte Gitter sogar 46 Knoten weniger als das uniform aufgelöste -- ist somit auch bei formaler Betrachtung der positive Nutzen von Gitterverfeinerung zur Simulation der Zylinderumströmung klar demonstriert. Wir erhalten bei leicht geringerer Anzahl von Knoten und somit näherungsweise gleichem Speicherbedarf ein deutlich besseres Simulationsergebnis.
+\bigskip
+
+Als weiteren Vergleich betrachten wir die entscheidenden maximalen Widerstands- und Auftriebskoeffizienten \(\widehat{c_w}\) bzw. \(\widehat{c_l}\) eines uniform mit \(N=40\), d.h. der maximalen lokalen Auflösung unseres problembewusst verfeinerten Gitters entsprechend, aufgelösten Gitters.
+Auch im Vergleich mit diesem 145314 Knoten umfassenden Gitter bewähren sich die, mit nur etwa einem Zehntel der Knoten gewonnenen, Ergebnisse der verfeinerten Simulation:
+
+\begin{figure}[h]
+\centering
+\begin{tabular}{l l l l l}
+& Uniform & Verfeinert & Referenzintervall \cite{SchaeferTurek96} \\
+\hline
+\hline
+\(\widehat{c_w}\) & 3.28433 & 3.21927 & \([3.22,\ 3.24]\) \\
+\(|\widehat{c_w}-3.23|\) & 0.05433 & 0.01073 & [0, 0.01] \\
+\hline
+\(\widehat{c_l}\) & 1.07046 & 1.10359 & \([0.99,\ 1.01]\) \\
+\(|\widehat{c_l}-1.0|\) & 0.07046 & 0.10359 & [0, 0.01] \\
+\hline
+\(\Delta P\) & 2.5793 & 2.44285 & \([2.46,\ 2.5]\) \\
+\(|\Delta P-2.48|\) & 0.0993 & 0.03715 & [0, 0.02] \\
+\hline
+\hline
+Knotenanzahl & 145314 & 13454 & \\
+\end{tabular}
+\caption{Vergleichswerte zweier maximal \(N=40\) aufgelöster Gitter}
+\end{figure}
+
+\noindent
+Tatsächlich ist der Fehler des verfeinerten Gitters für Widerstandskoeffizient und Druckdifferenz sogar kleiner als der des uniformen Gitters mit ungleich mehr Knoten.
+
\newpage
\section{Fazit}
diff --git a/img/cylinder2d_deltap_comparison.tikz b/img/cylinder2d_deltap_comparison.tikz
index 59b1657..97ecd37 100644
--- a/img/cylinder2d_deltap_comparison.tikz
+++ b/img/cylinder2d_deltap_comparison.tikz
@@ -1,6 +1,7 @@
\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
+\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv}\uniformHighRes
\begin{axis}[
scale only axis,
diff --git a/img/cylinder2d_drag_comparison.tikz b/img/cylinder2d_drag_comparison.tikz
index 8806b50..98336ec 100644
--- a/img/cylinder2d_drag_comparison.tikz
+++ b/img/cylinder2d_drag_comparison.tikz
@@ -1,6 +1,7 @@
\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
+\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv}\uniformHighRes
\begin{axis}[
scale only axis,
diff --git a/img/cylinder2d_lift_comparison.tikz b/img/cylinder2d_lift_comparison.tikz
index f143494..644a6b8 100644
--- a/img/cylinder2d_lift_comparison.tikz
+++ b/img/cylinder2d_lift_comparison.tikz
@@ -1,6 +1,7 @@
\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
+\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv}\uniformHighRes
\begin{axis}[
scale only axis,
diff --git a/img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv b/img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv
new file mode 100644
index 0000000..22eabb0
--- /dev/null
+++ b/img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv
@@ -0,0 +1,1602 @@
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