From 5f92c1dbea7532068edadbc64b1fcebecd6931f8 Mon Sep 17 00:00:00 2001 From: Adrian Kummerlaender Date: Wed, 20 Feb 2019 11:27:40 +0100 Subject: Localize decimal numbers --- content.tex | 26 +- img/common/velocity_fluid.gnuplot | 1 + img/cylinder2d_deltap_comparison.tikz | 5 +- img/cylinder2d_drag_comparison.tikz | 2 +- img/cylinder2d_high_res_comparsion.tikz | 21 +- img/cylinder2d_overview.tikz | 4 +- ...nerously_refined_n15_re100_drag_lift_deltap.csv | 1613 ++++++++++++++++++++ ...nerously_refined_n20_re100_drag_lift_deltap.csv | 1602 +++++++++++++++++++ ...nerously_refined_n25_re100_drag_lift_deltap.csv | 1606 +++++++++++++++++++ ...nerously_refined_n30_re100_drag_lift_deltap.csv | 1602 +++++++++++++++++++ ...mized_refinement_n40_re100_drag_lift_deltap.csv | 349 +++++ img/massloss_interpolation_plot.tikz | 4 +- img/poiseuille2d_error_comparison.tikz | 8 +- img/poiseuille2d_grid.tikz | 6 +- img/poiseuille2d_velocity_grid.tikz | 9 +- img/poiseuille2d_velocity_outflow.tikz | 5 +- ...inder2d_improved_grid_n20_re100_16s_knudsen.pdf | Bin 96793 -> 96793 bytes ..._low_resolution_outflow_refine_n5_re100_16s.pdf | Bin 95974 -> 95975 bytes ...ylinder2d_optimized_refinement_n5_re100_16s.pdf | Bin 264964 -> 264965 bytes ...d_optimized_refinement_n5_re100_16s_knudsen.pdf | Bin 91235 -> 91235 bytes .../cylinder2d_single_refinement_n20_re100_16s.pdf | Bin 588263 -> 588263 bytes ...r2d_single_refinement_n20_re100_16s_knudsen.pdf | Bin 98478 -> 98478 bytes img/static/cylinder2d_unrefined_n12_re100_16s.pdf | Bin 230847 -> 230847 bytes img/static/cylinder2d_unrefined_n20_re100_16s.pdf | Bin 305191 -> 305191 bytes .../cylinder2d_unrefined_n20_re100_16s_knudsen.pdf | Bin 80479 -> 80479 bytes img/static/cylinder2d_unrefined_n40_re100_16s.pdf | Bin 895747 -> 895747 bytes .../cylinder2d_unrefined_n40_re100_16s_knudsen.pdf | Bin 84684 -> 84684 bytes main.tex | 7 + shell.nix | 1 + 29 files changed, 6837 insertions(+), 34 deletions(-) create mode 100644 img/data/cylinder2d_generously_refined_n15_re100_drag_lift_deltap.csv create mode 100644 img/data/cylinder2d_generously_refined_n20_re100_drag_lift_deltap.csv create mode 100644 img/data/cylinder2d_generously_refined_n25_re100_drag_lift_deltap.csv create mode 100644 img/data/cylinder2d_generously_refined_n30_re100_drag_lift_deltap.csv diff --git a/content.tex b/content.tex index 0111c9d..3a9152d 100644 --- a/content.tex +++ b/content.tex @@ -850,9 +850,8 @@ Mit \(u_\text{max}:=1\) vereinfacht sich damit die analytische Lösung der \(x\) Das Geschwindigkeitsprofil des Poiseuille-Flusses ist also parabelförmig. \end{Definition} -Wir wollen in einem \(1 \times 4\) Längeneinheiten bemessenden Rohr einen Poiseuille-Fluss simulieren. Als Auflösung einer Längeneinheit sei dabei \(N=10\) gewählt, was in der Gitterdiskretisierung durch \(11 \times 21\) grobe und \(21 \times 43\) feine Knoten abgebildet wird. - -In Abbildung~\ref{fig:PoiseuilleGridSetup} sehen wir das resultierende Gitter zusammen mit den zugewiesenen Materialzahlen. Wand- und Einflusszellen werden nach dieser Vorlage mit lokalen Geschwindigkeitsrandbedingungen umgesetzt. Während für den Einfluss dabei das Geschwindigkeitsprofil der analytischen Poiseuille-Lösung vorausgesetzt wird, erhält der Ausfluss eine Druckrandbedingung. Die noch verbleibenden gewöhnlichen Fluidzellen erfahren, abgesehen von den üblichen Kollisions- und Strömungsschritten, keine besondere Behandlung. +Wir wollen in einem \(1 \times 4\) Meter bemessenden Rohr einen Poiseuille-Fluss simulieren. Als Auflösung einer Längeneinheit sei dabei \(N=10\) gewählt, was in der Diskretisierung durch \(11 \times 21\) grobe und \(21 \times 43\) feine Knoten abgebildet wird. +In Abbildung~\ref{fig:PoiseuilleGridSetup} sehen wir das resultierende Gitter zusammen mit den zugewiesenen Materialzahlen. Wand- und Einflusszellen werden nach dieser Vorlage mit lokalen Geschwindigkeitsrandbedingungen umgesetzt. Während für den Einfluss dabei das Geschwindigkeitsprofil der analytischen Poiseuille-Lösung vorausgesetzt wird, erhält der Ausfluss eine Druckrandbedingung. \begin{figure}[H] \begin{adjustbox}{center} @@ -862,7 +861,7 @@ In Abbildung~\ref{fig:PoiseuilleGridSetup} sehen wir das resultierende Gitter zu \label{fig:PoiseuilleGridSetup} \end{figure} -Neben diesen knotenspezifischen Eigenschaften sei \(u=0.01\) die charateristische Geschwindigkeit in Lattice-Einheiten und \(\text{Re}=10\) die modellierte Reynolds-Zahl. Erstellen wir unsere grobe \class{Grid2D} Instanz mit diesen, die Relaxionszeit \(\tau\) fixierenden, Werten und führen die Simulation bis zur Konvergenz aus, erblicken wir bei geeigneter Aufbereitung in ParaView~\cite{paraview05} schließlich das in Abbildung~\ref{fig:PoiseuilleVelocityGrid} ersichtliche Strömungsbild. Konvergenz bedeutet in diesem Kontext, dass die durchschnittliche Energie des feinen Gitters unter einen Residuumswert, hier \(1\mathrm{e}{-5}\), gefallen ist. +Neben diesen knotenspezifischen Eigenschaften sei \(u=\num[round-mode=off]{0.01}\) die charateristische Geschwindigkeit in Lattice-Einheiten und \(\text{Re}=10\) die modellierte Reynolds-Zahl. Erstellen wir unsere grobe \class{Grid2D} Instanz mit diesen, die Relaxionszeit \(\tau\) fixierenden, Werten und führen die Simulation bis zur Konvergenz aus, erblicken wir bei geeigneter Aufbereitung in ParaView~\cite{paraview05} schließlich das in Abbildung~\ref{fig:PoiseuilleVelocityGrid} ersichtliche Strömungsbild. Konvergenz bedeutet in diesem Kontext, dass die durchschnittliche Energie des feinen Gitters unter einen Residuumswert, hier \num{1e-5}, gefallen ist. \begin{figure}[h] \begin{adjustbox}{center} @@ -872,7 +871,7 @@ Neben diesen knotenspezifischen Eigenschaften sei \(u=0.01\) die charateristisch \label{fig:PoiseuilleVelocityGrid} \end{figure} -Bei erster Betrachtung lässt sich erkennen, dass die Strömung den Gitterübergang subjektiv ideal bestritten hat. Es treten also keine ungewöhnlichen Artefakte im Geschwindigkeitsbild auf und dieses setzt sich nach dem Übergang in, bis auf die neuen Zwischenwerte, unveränderter Weise fort. Tatsächlich ist bei Interpolation der Knotenzwischenbereiche zur Bildung einer geschlossenen Fläche kein Gitterübergang erkennbar. +Bei erster Betrachtung lässt sich erkennen, dass die Strömung den Gitterübergang subjektiv ideal bestritten hat. Es treten also keine ungewöhnlichen Artefakte im Geschwindigkeitsbild auf und dieses setzt sich nach dem Übergang in, bis auf die neuen Zwischenwerte, unveränderter Weise fort. Tatsächlich ist bei Bildung einer geschlossenen Fläche durch Interpolation der Zwischenbereiche kein Gitterübergang erkennbar. \newpage \subsubsection{Vergleich mit der analytischen Lösung} @@ -1143,14 +1142,14 @@ Auch im Vergleich mit diesem 145314 Knoten umfassenden Gitter bewähren sich die & 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] \\ +\(\widehat{c_w}\) & \num{3.28433} & \num{3.21927} & \([\num{3.22},\ \num{3.24}]\) \\ +\(|\widehat{c_w}-\num{3.23}|\) & \num{0.05433} & \num{0.01073} & [\num{0}, \num{0.01}] \\ \hline -\(\widehat{c_a}\) & 1.07046 & 1.10359 & \([0.99,\ 1.01]\) \\ -\(|\widehat{c_a}-1.0|\) & 0.07046 & 0.10359 & [0, 0.01] \\ +\(\widehat{c_a}\) & \num{1.07046} & \num{1.10359} & \([\num{0.99},\ \num{1.01}]\) \\ +\(|\widehat{c_a}-1.0|\) & \num{0.07046} & \num{0.10359} & [\num{0}, \num{0.01}] \\ \hline -\(\Delta P\) & 2.5793 & 2.44285 & \([2.46,\ 2.5]\) \\ -\(|\Delta P-2.48|\) & 0.0993 & 0.03715 & [0, 0.02] \\ +\(\Delta P\) & \num{2.5793} & \num{2.44285} & \([\num{2.46},\ \num{2.5}]\) \\ +\(|\Delta P-2.48|\) & \num{0.0993} & \num{0.03715} & [\num{0}, \num{0.02}] \\ \hline \hline Knotenanzahl & 145314 & 13454 & \\ @@ -1175,5 +1174,10 @@ Dazu sehen wir in Abbildung~\ref{fig:142000nodes} die charakteristischen Messwer \label{fig:142000nodes} \end{figure} +\begin{figure}[H] +\centering +\input{img/cylinder2d_generously_refined_comparison.tikz} +\end{figure} + \newpage \section{Fazit} diff --git a/img/common/velocity_fluid.gnuplot b/img/common/velocity_fluid.gnuplot index 5535111..c0db2a9 100644 --- a/img/common/velocity_fluid.gnuplot +++ b/img/common/velocity_fluid.gnuplot @@ -7,6 +7,7 @@ set output 'tmp/'.plotname.'.png' load 'common/moreland.pal' set datafile separator ',' +set decimalsign ',' set size 1,1 set margin 0,0,0,0 diff --git a/img/cylinder2d_deltap_comparison.tikz b/img/cylinder2d_deltap_comparison.tikz index 97ecd37..2d6fd99 100644 --- a/img/cylinder2d_deltap_comparison.tikz +++ b/img/cylinder2d_deltap_comparison.tikz @@ -15,7 +15,8 @@ xlabel={Simulierte physikalische Zeit}, ylabel={Druckdifferenz}, x unit=s, - y unit=N/m^2 + y unit=N/m^2, + y tick label style={/pgf/number format/.cd, use comma} ] \addplot[ @@ -35,7 +36,7 @@ \addlegendentry {Problembezogen verfeinertes \(N=5\) Gitter}; \addplot[color=black]{2.48}; -\addlegendentry {Gemittelte Referenzlösung \(\Delta P := 2.48\)}; +\addlegendentry {Gemittelte Referenzlösung \(\Delta P := \num{2.48}\)}; \end{axis} \end{tikzpicture} diff --git a/img/cylinder2d_drag_comparison.tikz b/img/cylinder2d_drag_comparison.tikz index 98336ec..ee0c783 100644 --- a/img/cylinder2d_drag_comparison.tikz +++ b/img/cylinder2d_drag_comparison.tikz @@ -34,7 +34,7 @@ \addlegendentry {Problembezogen verfeinertes \(N=5\) Gitter}; \addplot[color=black]{3.23}; -\addlegendentry {Gemittelte Referenzlösung \(c_\text{Dmax} := 3.23\)}; +\addlegendentry {Gemittelte Referenzlösung \(c_\text{Dmax} := \num{3.23}\)}; \end{axis} \end{tikzpicture} diff --git a/img/cylinder2d_high_res_comparsion.tikz b/img/cylinder2d_high_res_comparsion.tikz index aa8b2a7..9bde49b 100644 --- a/img/cylinder2d_high_res_comparsion.tikz +++ b/img/cylinder2d_high_res_comparsion.tikz @@ -1,6 +1,7 @@ \begin{tikzpicture} \pgfplotstableread[col sep=comma]{img/data/cylinder2d_optimized_refinement_n40_re100_drag_lift_deltap.csv}\refined -\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv}\uniformVeryHigh +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n40_re100_drag_lift_deltap.csv}\uniformHigh +\pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n80_re100_drag_lift_deltap.csv}\uniformVeryHigh \pgfplotstableread[col sep=comma]{img/data/cylinder2d_unrefined_n160_re100_drag_lift_deltap.csv}\uniformVeryVeryHigh \begin{axis}[ @@ -15,11 +16,13 @@ ylabel={Widerstandskoeffizient}, ylabel absolute, every axis y label/.append style={yshift=0.4cm} ] + \addplot[thick,color=black]{3.23}; -\addlegendentry {\(\widehat{c_w} := 3.23\)}; +\addlegendentry {\(\widehat{c_w} := \num[round-mode=off]{3.23}\)}; \addplot[color=blue!50!white,thin ] table [x expr=\thisrow{time}, y=drag] {\uniformVeryVeryHigh}; \addplot[color=red!50!white,thin ] table [x expr=\thisrow{time}, y=drag] {\uniformVeryHigh}; \addplot[color=green!70!black,thin] table [x expr=8*\thisrow{time}, y=drag] {\refined}; + \end{axis} \begin{axis}[ @@ -35,11 +38,13 @@ ylabel={Auftriebskoeffizient}, ylabel absolute, every axis y label/.append style={yshift=0.4cm} ] + \addplot[thick,color=black]{1.0}; \addlegendentry {\(\widehat{c_a} := 1\)}; \addplot[color=blue!50!white,thin ] table [x expr=\thisrow{time}, y=lift] {\uniformVeryVeryHigh}; \addplot[color=red!50!white,thin ] table [x expr=\thisrow{time}, y=lift] {\uniformVeryHigh}; \addplot[color=green!70!black,thin] table [x expr=8*\thisrow{time}, y=lift] {\refined}; + \end{axis} \begin{axis}[ @@ -58,14 +63,16 @@ y unit=N/m^2, ylabel absolute, every axis y label/.append style={yshift=0.4cm} ] + +\addplot[thick,color=black]{2.48}; +\addlegendentry {\(\Delta P := \num[round-mode=off]{2.48}\)}; \addplot[color=blue!50!white,thin ] table [x expr=\thisrow{time}, y=deltap] {\uniformVeryVeryHigh}; -\addlegendentry {Uniformes \(N=160\) Gitter mit 2298014 Knoten}; +\addlegendentry {Uniformes \(N=160\) Gitter mit \(\sim 2300000\) Knoten}; \addplot[color=red!50!white,thin ] table [x expr=\thisrow{time}, y=deltap] {\uniformVeryHigh}; -\addlegendentry {Uniformes \(N=40\) Gitter mit 576758 Knoten}; +\addlegendentry {Uniformes \(N=80\) Gitter mit \(\sim 577000\) Knoten}; \addplot[color=green!70!black,thin] table [x expr=8*\thisrow{time}, y=deltap] {\refined}; -\addlegendentry {Verfeinertes \(N=40\) Gitter mit 787592 Knoten}; -\addplot[thick,color=black]{2.48}; -\addlegendentry {\(\Delta P := 2.48\)}; +\addlegendentry {Verfeinertes \(N=40\) Gitter mit \(\sim 790000\) Knoten}; + \end{axis} \end{tikzpicture} diff --git a/img/cylinder2d_overview.tikz b/img/cylinder2d_overview.tikz index 3fa0da8..d77c1c1 100644 --- a/img/cylinder2d_overview.tikz +++ b/img/cylinder2d_overview.tikz @@ -10,8 +10,8 @@ \draw[very thick,fill=gray!20!white] (2,2) circle (0.5); \draw[Latex-Latex,thin] (3,1.5) -- (3,2.5) node[pos=0.5,right] {\(D\)}; -\draw[Latex-Latex,thin] (3,0) -- (3,1.5) node[pos=0.5,right] {\(1.5 D\)}; -\draw[Latex-Latex,thin] (3,2.5) -- (3,4.1) node[pos=0.5,right] {\(1.6 D\)}; +\draw[Latex-Latex,thin] (3,0) -- (3,1.5) node[pos=0.5,right] {\(\num{1.5} D\)}; +\draw[Latex-Latex,thin] (3,2.5) -- (3,4.1) node[pos=0.5,right] {\(\num{1.6} D\)}; \draw[Latex-Latex,thin] (0,-0.5) -- (2,-0.5) node[pos=0.5,below] {\(2 D\)}; \draw[Latex-Latex,thin] (2,-0.5) -- (22,-0.5) node[pos=0.5,below] {\(20 D\)}; diff --git a/img/data/cylinder2d_generously_refined_n15_re100_drag_lift_deltap.csv 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