commit 4de4c0eea0933830036bb80094c57cd74396d3d3 parent fb0a6002758be2ffda31f868a4ad86229feb6b20 Author: Ivan Gankevich <i.gankevich@spbu.ru> Date: Sat, 14 Mar 2020 17:10:25 +0300 Verification graph. Diffstat:
| Makefile | | | 5 | +++++ |
| gnuplot/rdbu.pal | | | 25 | +++++++++++++++++++++++++ |
| gnuplot/verification.gnuplot | | | 18 | ++++++++++++++++++ |
| gnuplot/wind.orig | | | 1232 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| gnuplot/wind.our | | | 1232 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| main.tex | | | 13 | ++++++++++++- |
6 files changed, 2524 insertions(+), 1 deletion(-)
diff --git a/Makefile b/Makefile @@ -15,6 +15,7 @@ all: build/$(NAME).pdf all: build/$(SLIDES).pdf build/$(NAME).pdf: build/inkscape/law-of-reflection.eps +build/$(NAME).pdf: build/gnuplot/verification.eps build/$(NAME).pdf: main.tex build/$(NAME).pdf: @echo " LATEX $<" @@ -31,6 +32,10 @@ build/inkscape/%.eps: graphics/inkscape/%.svg @mkdir -p build/inkscape inkscape -z --export-eps=$@ $< +build/gnuplot/%.svg: gnuplot/%.gnuplot + @mkdir -p build/gnuplot + gnuplot -d $< + build: @mkdir -p build diff --git a/gnuplot/rdbu.pal b/gnuplot/rdbu.pal @@ -0,0 +1,25 @@ +# line styles for ColorBrewer RdBu +# for use with divering data +# provides 8 colors with red low, white middle, and blue high +# compatible with gnuplot >=4.2 +# author: Anna Schneider + +# line styles +set style line 1 lt 1 lc rgb '#B2182B' # red +set style line 2 lt 1 lc rgb '#D6604D' # red-orange +set style line 3 lt 1 lc rgb '#F4A582' # +set style line 4 lt 1 lc rgb '#FDDBC7' # pale orange +set style line 5 lt 1 lc rgb '#D1E5F0' # pale blue +set style line 6 lt 1 lc rgb '#92C5DE' # +set style line 7 lt 1 lc rgb '#4393C3' # medium blue +set style line 8 lt 1 lc rgb '#2166AC' # dark blue + +# palette +set palette defined (0 '#2166AC',\ + 1 '#4393C3',\ + 2 '#92C5DE',\ + 3 '#D1E5F0',\ + 4 '#FDDBC7',\ + 5 '#F4A582',\ + 6 '#D6604D',\ + 7 '#B2182B') diff --git a/gnuplot/verification.gnuplot b/gnuplot/verification.gnuplot @@ -0,0 +1,18 @@ +set terminal svg dynamic size 1080/4*1.9, 1080/4 round enhanced font 'Liberation Serif, 12' +set output "build/gnuplot/verification.svg" +#set key outside top center +unset key +set xtics -50,25,50 out nomirror +set ytics -50,25,50 out nomirror +set xrange [-52:52] +set yrange [-52:52] +set border 1+2 +set size square +set size ratio -1 +load 'gnuplot/rdbu.pal' +set cbrange [0:100] +s = 0.05 +set multiplot layout 1,2 +set object 1 circle front at 0,0 size 54.8858/2 fillcolor rgb "black" lw 0.5 +plot 'gnuplot/wind.orig' using 1:2:($3*s):($4*s):(sqrt($3**2+$4**2)) with vectors lw 0.1 lc palette +plot 'gnuplot/wind.our' using 1:2:($3*s):($4*s):(sqrt($3**2+$4**2)) with vectors lw 0.1 lc palette diff --git a/gnuplot/wind.orig b/gnuplot/wind.orig @@ -0,0 +1,1232 @@ +-50 -50 50 -7.53113 +-50 -47.4359 49.5831 -7.91626 +-50 -44.8718 49.1007 -8.29432 +-50 -42.3077 48.5471 -8.65659 +-50 -39.7436 47.9174 -8.99232 +-50 -37.1795 47.2077 -9.28864 +-50 -34.6154 46.4159 -9.53043 +-50 -32.0513 45.5427 -9.70051 +-50 -29.4872 44.5922 -9.77989 +-50 -26.9231 43.5725 -9.74844 +-50 -24.359 42.4969 -9.5858 +-50 -21.7949 41.3847 -9.27269 +-50 -19.2308 40.2605 -8.79258 +-50 -16.6667 39.1552 -8.13362 +-50 -14.1026 38.104 -7.29055 +-50 -11.5385 37.1455 -6.26659 +-50 -8.97436 36.3187 -5.07472 +-50 -6.41025 35.6606 -3.73822 +-50 -3.84615 35.2025 -2.29009 +-50 -1.28205 34.9674 -0.771408 +-50 1.28205 34.9674 0.77141 +-50 3.84616 35.2025 2.29009 +-50 6.41026 35.6606 3.73822 +-50 8.97436 36.3187 5.07473 +-50 11.5385 37.1455 6.26659 +-50 14.1026 38.104 7.29055 +-50 16.6667 39.1552 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different term \(s\) than the solution for potential flow around a cylinder which makes reflected velocity term reach maximum value for the point on the boundary, and for the point near the boundary the solution includes reflected velocity vectors for -each panel. +each panel. We compared both solutions (see fig.~\ref{fig-verification}) for a +cylinder with \(R=27.4429\), and discovered that maximum root mean square error +between the two is less than 1\%. + +\begin{figure} + \centering + \includegraphics{build/gnuplot/verification.eps} + \caption{Wind velocity fields: left --- known + solution~\eqref{eq-solution-cylinder}, right --- our + solution~\eqref{eq-solution-near-the-boundary}.\label{fig-verification}} +\end{figure} + \section{Conclusion}