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authorAdrian Kummerlaender2019-02-20 11:27:40 +0100
committerAdrian Kummerlaender2019-02-20 11:28:20 +0100
commit5f92c1dbea7532068edadbc64b1fcebecd6931f8 (patch)
tree8e939f8485cb8eb4f2b47a958b653f639f566e36
parent46efb766d57f76cebd10819d4bf3c3460bd17264 (diff)
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Localize decimal numbers
-rw-r--r--content.tex26
-rw-r--r--img/common/velocity_fluid.gnuplot1
-rw-r--r--img/cylinder2d_deltap_comparison.tikz5
-rw-r--r--img/cylinder2d_drag_comparison.tikz2
-rw-r--r--img/cylinder2d_high_res_comparsion.tikz21
-rw-r--r--img/cylinder2d_overview.tikz4
-rw-r--r--img/data/cylinder2d_generously_refined_n15_re100_drag_lift_deltap.csv1613
-rw-r--r--img/data/cylinder2d_generously_refined_n20_re100_drag_lift_deltap.csv1602
-rw-r--r--img/data/cylinder2d_generously_refined_n25_re100_drag_lift_deltap.csv1606
-rw-r--r--img/data/cylinder2d_generously_refined_n30_re100_drag_lift_deltap.csv1602
-rw-r--r--img/data/cylinder2d_optimized_refinement_n40_re100_drag_lift_deltap.csv349
-rw-r--r--img/massloss_interpolation_plot.tikz4
-rw-r--r--img/poiseuille2d_error_comparison.tikz8
-rw-r--r--img/poiseuille2d_grid.tikz6
-rw-r--r--img/poiseuille2d_velocity_grid.tikz9
-rw-r--r--img/poiseuille2d_velocity_outflow.tikz5
-rw-r--r--img/static/cylinder2d_improved_grid_n20_re100_16s_knudsen.pdfbin96793 -> 96793 bytes
-rw-r--r--img/static/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.pdfbin95974 -> 95975 bytes
-rw-r--r--img/static/cylinder2d_optimized_refinement_n5_re100_16s.pdfbin264964 -> 264965 bytes
-rw-r--r--img/static/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.pdfbin91235 -> 91235 bytes
-rw-r--r--img/static/cylinder2d_single_refinement_n20_re100_16s.pdfbin588263 -> 588263 bytes
-rw-r--r--img/static/cylinder2d_single_refinement_n20_re100_16s_knudsen.pdfbin98478 -> 98478 bytes
-rw-r--r--img/static/cylinder2d_unrefined_n12_re100_16s.pdfbin230847 -> 230847 bytes
-rw-r--r--img/static/cylinder2d_unrefined_n20_re100_16s.pdfbin305191 -> 305191 bytes
-rw-r--r--img/static/cylinder2d_unrefined_n20_re100_16s_knudsen.pdfbin80479 -> 80479 bytes
-rw-r--r--img/static/cylinder2d_unrefined_n40_re100_16s.pdfbin895747 -> 895747 bytes
-rw-r--r--img/static/cylinder2d_unrefined_n40_re100_16s_knudsen.pdfbin84684 -> 84684 bytes
-rw-r--r--main.tex7
-rw-r--r--shell.nix1
29 files changed, 6837 insertions, 34 deletions
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 b/img/data/cylinder2d_generously_refined_n15_re100_drag_lift_deltap.csv
new file mode 100644
index 0000000..df3ffdf
--- /dev/null
+++ b/img/data/cylinder2d_generously_refined_n15_re100_drag_lift_deltap.csv
@@ -0,0 +1,1613 @@
+time,drag,lift,deltap
+0,0,0,0
+0.00124074,2.16707e-07,-1.01615e-09,1.41561e-07
+0.00248148,5.66404e-06,-2.32384e-08,3.48643e-06
+0.00372222,2.07988e-05,-4.13144e-08,1.26355e-05
+0.00496296,4.51912e-05,-7.25249e-08,2.64518e-05
+0.0062037,8.05954e-05,-1.30149e-07,4.81813e-05
+0.00744444,0.000125882,-1.51336e-07,7.29354e-05
+0.00868519,0.000179798,-2.59974e-07,0.000104258
+0.00992593,0.000249092,-2.85972e-07,0.000144944
+0.0111667,0.000322546,-3.82066e-07,0.000182332
+0.0124074,0.000413101,-5.36216e-07,0.000238647
+0.0136481,0.000513467,-4.832e-07,0.000289239
+0.0148889,0.000618901,-8.09399e-07,0.000349125
+0.0161296,0.000750258,-7.48793e-07,0.000425646
+0.0173704,0.000874775,-9.12487e-07,0.000483313
+0.0186111,0.00102628,-1.23767e-06,0.000579434
+0.0198519,0.00118623,-9.88473e-07,0.000654675
+0.0210926,0.00134556,-1.62793e-06,0.000743902
+0.0223333,0.00155243,-1.41798e-06,0.000864309
+0.0235741,0.00174183,-1.65263e-06,0.000946437
+0.0248148,0.00197321,-2.19395e-06,0.00109526
+0.0260556,0.00221027,-1.6465e-06,0.00120166
+0.0272963,0.00243669,-2.70767e-06,0.00132701
+0.028537,0.002725,-2.26102e-06,0.00149418
+0.0297778,0.00296786,-2.56064e-06,0.00158973
+0.0310185,0.00326876,-3.37514e-06,0.00178677
+0.0322593,0.00357276,-2.42635e-06,0.00191507
+0.0335,0.00385458,-3.98675e-06,0.00206945
+0.0347407,0.00422257,-3.24489e-06,0.00228287
+0.0359815,0.00451762,-3.62553e-06,0.00238808
+0.0372222,0.00489117,-4.7446e-06,0.00263737
+0.038463,0.00526355,-3.3024e-06,0.00278564
+0.0397037,0.00559963,-5.4718e-06,0.00296833
+0.0409444,0.00605,-4.35728e-06,0.00323001
+0.0421852,0.00639465,-4.81179e-06,0.00334038
+0.0434259,0.00683807,-6.30127e-06,0.00364226
+0.0446667,0.00726866,-4.2744e-06,0.00380186
+0.0459074,0.00764363,-7.12343e-06,0.00400396
+0.0471481,0.00816632,-5.58634e-06,0.00430873
+0.0483889,0.00854746,-6.1322e-06,0.00441428
+0.0496296,0.00905768,-8.02073e-06,0.00476959
+0.0508704,0.0095552,-5.3359e-06,0.00494393
+0.0521111,0.00998171,-8.96114e-06,0.00517342
+0.0533519,0.0105919,-6.93372e-06,0.00553075
+0.0545926,0.0110188,-7.57015e-06,0.00563438
+0.0558333,0.0116049,-9.90253e-06,0.00605014
+0.0570741,0.0121718,-6.4789e-06,0.00623808
+0.0583148,0.0126479,-1.09423e-05,0.00649377
+0.0595556,0.0133479,-8.36819e-06,0.00690521
+0.0607963,0.0138195,-9.11157e-06,0.00700391
+0.062037,0.014484,-1.19074e-05,0.00748331
+0.0632778,0.0151227,-7.66954e-06,0.00768405
+0.0645185,0.0156511,-1.30517e-05,0.00796762
+0.0657593,0.0164518,-9.86902e-06,0.00843995
+0.067,0.01698,-1.07163e-05,0.0085384
+0.0682407,0.0177372,-1.40013e-05,0.00909125
+0.0694815,0.0184582,-8.87881e-06,0.00930843
+0.0707222,0.0190443,-1.52312e-05,0.00962269
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+0.0732037,0.0205145,-1.2334e-05,0.0102417
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+0.0806481,0.0253069,-1.82353e-05,0.0127823
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diff --git a/img/data/cylinder2d_generously_refined_n20_re100_drag_lift_deltap.csv b/img/data/cylinder2d_generously_refined_n20_re100_drag_lift_deltap.csv
new file mode 100644
index 0000000..9801aea
--- /dev/null
+++ b/img/data/cylinder2d_generously_refined_n20_re100_drag_lift_deltap.csv
@@ -0,0 +1,1602 @@
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diff --git a/img/data/cylinder2d_generously_refined_n25_re100_drag_lift_deltap.csv b/img/data/cylinder2d_generously_refined_n25_re100_drag_lift_deltap.csv
new file mode 100644
index 0000000..f6209d7
--- /dev/null
+++ b/img/data/cylinder2d_generously_refined_n25_re100_drag_lift_deltap.csv
@@ -0,0 +1,1606 @@
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diff --git a/img/data/cylinder2d_generously_refined_n30_re100_drag_lift_deltap.csv b/img/data/cylinder2d_generously_refined_n30_re100_drag_lift_deltap.csv
new file mode 100644
index 0000000..b414ba4
--- /dev/null
+++ b/img/data/cylinder2d_generously_refined_n30_re100_drag_lift_deltap.csv
@@ -0,0 +1,1602 @@
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diff --git a/img/data/cylinder2d_optimized_refinement_n40_re100_drag_lift_deltap.csv b/img/data/cylinder2d_optimized_refinement_n40_re100_drag_lift_deltap.csv
index 4db1ec3..049eaa1 100644
--- a/img/data/cylinder2d_optimized_refinement_n40_re100_drag_lift_deltap.csv
+++ b/img/data/cylinder2d_optimized_refinement_n40_re100_drag_lift_deltap.csv
@@ -1251,3 +1251,352 @@ time,drag,lift,deltap
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+1.8675,3.19665,-1.01008,2.45008
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+1.87,3.21262,-1.00768,2.47693
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+1.8775,3.17223,-0.269384,2.44275
+1.87875,3.16176,-0.0823571,2.42717
+1.88,3.15418,0.107406,2.41364
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+1.88375,3.15659,0.626137,2.4016
+1.885,3.16545,0.761025,2.40919
+1.88625,3.17676,0.867902,2.42154
+1.8875,3.18892,0.942878,2.43685
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+1.89,3.20899,0.988071,2.46729
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+1.96875,3.16792,0.788471,2.41169
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+1.99875,3.20692,-0.770787,2.48225
+2,3.19748,-0.632696,2.47345
diff --git a/img/massloss_interpolation_plot.tikz b/img/massloss_interpolation_plot.tikz
index 501f553..2626c26 100644
--- a/img/massloss_interpolation_plot.tikz
+++ b/img/massloss_interpolation_plot.tikz
@@ -9,7 +9,9 @@
xlabel=Horizontale Kanalposition,
ylabel=Druck,
y unit=N/m^2,
- x unit=m
+ x unit=m,
+ x tick label style={/pgf/number format/.cd, use comma},
+ y tick label style={/pgf/number format/.cd, use comma}
]
\addplot table[
diff --git a/img/poiseuille2d_error_comparison.tikz b/img/poiseuille2d_error_comparison.tikz
index adde6c3..b28f579 100644
--- a/img/poiseuille2d_error_comparison.tikz
+++ b/img/poiseuille2d_error_comparison.tikz
@@ -43,14 +43,14 @@
& \begin{tikzpicture}
\draw (0,0) rectangle (4,1) node[pos=.5] {\(11 \times 41\)};
\end{tikzpicture}
-& 1.88337e-3 & 3.11534e-3 \\
+& \num{1.88337e-3} & \num{3.11534e-3} \\
\hline \\[-1.75ex]
\texttt{uN20}
& \begin{tikzpicture}
\draw (0,0) rectangle (4,1) node[pos=.5] {\(21 \times 81\)};
\end{tikzpicture}
-& 1.16253e-3 & 2.27404e-3 \\
+& \num{1.16253e-3} & \num{2.27404e-3} \\
\hline \\[-1.75ex]
\texttt{vN10A}
@@ -58,7 +58,7 @@
\draw (0,0) rectangle (2,1) node[pos=.5] {\(11 \times 21\)};
\draw (2,0) rectangle (4,1) node[pos=.5] {\(21 \times 43\)};
\end{tikzpicture}
-& 1.015925e-2 & 2.396855e-2 \\
+& \num{1.015925e-2} & \num{2.396855e-2} \\
\hline \\[-1.75ex]
\texttt{vN10B}
@@ -67,5 +67,5 @@
\draw (0,0) rectangle (4,1);
\draw (2,0.1) rectangle (3.9,0.9) node[pos=.5] {\(17 \times 41\)};
\end{tikzpicture}
-& 1.90948e-3 & 3.25338e-3 \\
+& \num{1.90948e-3} & \num{3.25338e-3} \\
\end{tabular}
diff --git a/img/poiseuille2d_grid.tikz b/img/poiseuille2d_grid.tikz
index 24fe56a..f29c206 100644
--- a/img/poiseuille2d_grid.tikz
+++ b/img/poiseuille2d_grid.tikz
@@ -1,11 +1,13 @@
\begin{tikzpicture}
\begin{axis}[
scale only axis,
- height=0.95*\textwidth/4,
- width=0.95*\textwidth,
+ height=\textwidth)/4,
+ width=\textwidth,
axis equal,
xmin=0, xmax=4,
ymin=0, ymax=1,
+ x tick label style={/pgf/number format/.cd, use comma},
+ y tick label style={/pgf/number format/.cd, use comma},
scatter/classes={
1={color=blue!50!white},
2={color=gray!70!black},
diff --git a/img/poiseuille2d_velocity_grid.tikz b/img/poiseuille2d_velocity_grid.tikz
index 86afa7b..8ff04ab 100644
--- a/img/poiseuille2d_velocity_grid.tikz
+++ b/img/poiseuille2d_velocity_grid.tikz
@@ -1,11 +1,13 @@
\begin{tikzpicture}
\begin{axis}[
scale only axis,
- height=0.95\textwidth)/4,
- width=0.95\textwidth,
+ height=\textwidth)/4,
+ width=\textwidth,
axis equal,
xmin=0, xmax=4,
ymin=0, ymax=1,
+ x tick label style={/pgf/number format/.cd, use comma},
+ y tick label style={/pgf/number format/.cd, use comma},
point meta=explicit,
colorbar,
colormap/RdYlBu-4,
@@ -17,10 +19,11 @@
colorbar horizontal,
colorbar style={
/pgf/number format/precision=2,
+ /pgf/number format/use comma,
at={(0.5,-0.2)},
anchor=north,
width=0.5*\pgfkeysvalueof{/pgfplots/parent axis width},
- ylabel=\(m/s\),
+ y unit=m/s,
y label style={
at={(axis description cs:1.3,0.5)},
rotate=-90,
diff --git a/img/poiseuille2d_velocity_outflow.tikz b/img/poiseuille2d_velocity_outflow.tikz
index 96eec84..b60c6ff 100644
--- a/img/poiseuille2d_velocity_outflow.tikz
+++ b/img/poiseuille2d_velocity_outflow.tikz
@@ -17,7 +17,9 @@
xlabel=\(y\)-Position,
xtick={0,0.25,0.5,0.75,1},
title=Geschwindigkeitsprofil,
- every axis plot/.append style={thick}
+ every axis plot/.append style={thick},
+ x tick label style={/pgf/number format/.cd, use comma},
+ y tick label style={/pgf/number format/.cd, use comma}
]
\addplot[
@@ -70,6 +72,7 @@
xshift=7cm,
scaled y ticks=false,
y tick label style={/pgf/number format/sci},
+ x tick label style={/pgf/number format/.cd, use comma},
ylabel=Fehler,
xlabel=\(y\)-Position,
yticklabel pos=right,
diff --git a/img/static/cylinder2d_improved_grid_n20_re100_16s_knudsen.pdf b/img/static/cylinder2d_improved_grid_n20_re100_16s_knudsen.pdf
index 3d4264b..be8ab6b 100644
--- a/img/static/cylinder2d_improved_grid_n20_re100_16s_knudsen.pdf
+++ b/img/static/cylinder2d_improved_grid_n20_re100_16s_knudsen.pdf
Binary files differ
diff --git a/img/static/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.pdf b/img/static/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.pdf
index 9822474..ef7d937 100644
--- a/img/static/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.pdf
+++ b/img/static/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.pdf
Binary files differ
diff --git a/img/static/cylinder2d_optimized_refinement_n5_re100_16s.pdf b/img/static/cylinder2d_optimized_refinement_n5_re100_16s.pdf
index 64e9366..2bb1a30 100644
--- a/img/static/cylinder2d_optimized_refinement_n5_re100_16s.pdf
+++ b/img/static/cylinder2d_optimized_refinement_n5_re100_16s.pdf
Binary files differ
diff --git a/img/static/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.pdf b/img/static/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.pdf
index 0a8e0a9..7cfa276 100644
--- a/img/static/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.pdf
+++ b/img/static/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.pdf
Binary files differ
diff --git a/img/static/cylinder2d_single_refinement_n20_re100_16s.pdf b/img/static/cylinder2d_single_refinement_n20_re100_16s.pdf
index b1598c9..c404855 100644
--- a/img/static/cylinder2d_single_refinement_n20_re100_16s.pdf
+++ b/img/static/cylinder2d_single_refinement_n20_re100_16s.pdf
Binary files differ
diff --git a/img/static/cylinder2d_single_refinement_n20_re100_16s_knudsen.pdf b/img/static/cylinder2d_single_refinement_n20_re100_16s_knudsen.pdf
index 74cc21c..1648d01 100644
--- a/img/static/cylinder2d_single_refinement_n20_re100_16s_knudsen.pdf
+++ b/img/static/cylinder2d_single_refinement_n20_re100_16s_knudsen.pdf
Binary files differ
diff --git a/img/static/cylinder2d_unrefined_n12_re100_16s.pdf b/img/static/cylinder2d_unrefined_n12_re100_16s.pdf
index 08935a8..b5d2aba 100644
--- a/img/static/cylinder2d_unrefined_n12_re100_16s.pdf
+++ b/img/static/cylinder2d_unrefined_n12_re100_16s.pdf
Binary files differ
diff --git a/img/static/cylinder2d_unrefined_n20_re100_16s.pdf b/img/static/cylinder2d_unrefined_n20_re100_16s.pdf
index fd66c43..3d9d1d9 100644
--- a/img/static/cylinder2d_unrefined_n20_re100_16s.pdf
+++ b/img/static/cylinder2d_unrefined_n20_re100_16s.pdf
Binary files differ
diff --git a/img/static/cylinder2d_unrefined_n20_re100_16s_knudsen.pdf b/img/static/cylinder2d_unrefined_n20_re100_16s_knudsen.pdf
index 45ca4f7..207b45e 100644
--- a/img/static/cylinder2d_unrefined_n20_re100_16s_knudsen.pdf
+++ b/img/static/cylinder2d_unrefined_n20_re100_16s_knudsen.pdf
Binary files differ
diff --git a/img/static/cylinder2d_unrefined_n40_re100_16s.pdf b/img/static/cylinder2d_unrefined_n40_re100_16s.pdf
index 785e2f5..84d9a6b 100644
--- a/img/static/cylinder2d_unrefined_n40_re100_16s.pdf
+++ b/img/static/cylinder2d_unrefined_n40_re100_16s.pdf
Binary files differ
diff --git a/img/static/cylinder2d_unrefined_n40_re100_16s_knudsen.pdf b/img/static/cylinder2d_unrefined_n40_re100_16s_knudsen.pdf
index 26fcee8..69e2f16 100644
--- a/img/static/cylinder2d_unrefined_n40_re100_16s_knudsen.pdf
+++ b/img/static/cylinder2d_unrefined_n40_re100_16s_knudsen.pdf
Binary files differ
diff --git a/main.tex b/main.tex
index 94708c3..e73fa84 100644
--- a/main.tex
+++ b/main.tex
@@ -10,6 +10,13 @@
\usepackage{enumitem}
\usepackage[outputdir=build]{minted}
+\usepackage{siunitx}
+\sisetup{
+ locale=DE,
+ round-mode=places,
+ round-precision=4
+}
+
\usemintedstyle{borland}
\setminted{
tabsize=2,
diff --git a/shell.nix b/shell.nix
index baf95a0..85ec95d 100644
--- a/shell.nix
+++ b/shell.nix
@@ -9,6 +9,7 @@ stdenv.mkDerivation rec {
inherit (texlive) scheme-small collection-langgerman latexmk
amsmath
cm-super
+ siunitx
enumitem
minted fvextra ifplatform framed
bibtex biblatex logreq xstring