commit b3f9e9803486997d450c57ed3d6e4448fe9aacce
parent ef2aeaab3cb1564f677436f16640c010a52a4d09
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Fri, 26 Jun 2020 17:10:51 +0300
Slides.
Diffstat:
6 files changed, 369 insertions(+), 6 deletions(-)
diff --git a/.gitignore b/.gitignore
@@ -1,4 +1,5 @@
/build
+CoA_Medium.eps
# Created by https://www.gitignore.io/api/vim,linux,latex
# Edit at https://www.gitignore.io/?templates=vim,linux,latex
diff --git a/Makefile b/Makefile
@@ -26,6 +26,16 @@ build/$(NAME).pdf:
@echo " LATEX $<"
@-$(LATEXMK) $(FLAGS) -f main.tex
+build/$(SLIDES).pdf: build/gnuplot/aurora.eps
+build/$(SLIDES).pdf: build/gnuplot/cylinder-1.eps
+build/$(SLIDES).pdf: build/gnuplot/cylinder-2.eps
+build/$(SLIDES).pdf: build/gnuplot/openmp.svg
+build/$(SLIDES).pdf: build/gnuplot/ship-roll.eps
+build/$(SLIDES).pdf: build/gnuplot/ship-velocity.eps
+build/$(SLIDES).pdf: build/inkscape/law-of-reflection.eps
+build/$(SLIDES).pdf: build/ships/aurora.eps
+build/$(SLIDES).pdf: build/ships/diogen.eps
+build/$(SLIDES).pdf: build/ships/micw.eps
build/$(SLIDES).pdf: slides.tex
@echo " LATEX $<"
@-$(LATEXMK) $(FLAGS) -xelatex -f $<
@@ -41,6 +51,14 @@ build/gnuplot/%.svg: gnuplot/%.gnuplot
@mkdir -p build/gnuplot
gnuplot -d $<
+build/gnuplot/cylinder-1.svg build/gnuplot/cylinder-2.svg: gnuplot/cylinder.gnuplot
+ @mkdir -p build/gnuplot
+ gnuplot -d $<
+
+build/gnuplot/ship-roll.svg build/gnuplot/ship-velocity.svg: gnuplot/ship-roll-velocity.gnuplot
+ @mkdir -p build/gnuplot
+ gnuplot -d $<
+
build/ships/diogen.svg: ships/diogen.gnuplot gnuplot/vessel.gnuplot
@mkdir -p build/ships
gnuplot -d -c gnuplot/vessel.gnuplot $< $@ Diogen
diff --git a/gnuplot/aurora.gnuplot b/gnuplot/aurora.gnuplot
@@ -0,0 +1,29 @@
+set terminal svg size 1920/4,1080/4 dynamic
+set hidden3d back offset 0 trianglepattern 3 undefined 1 altdiagonal bentover
+set view equal xyz
+set view ,,4
+#set object 1 rectangle from screen -0.1,-0.1 to screen 1.1,1.1 fillcolor rgb "#f0f0f0" behind
+unset key
+set title 'Aurora' offset 0,-2
+#unset border
+#unset xtics
+#unset ytics
+#unset ztics
+#load 'gnuplot/rdbu.pal'
+set ytics -20,20,20
+set ztics 0,10,40
+set palette gray
+set pm3d
+set style data pm3d
+unset colorbox
+set xrange [0:130]
+set yrange [-20:20]
+set zrange [*:20]
+set xzeroaxis
+set yzeroaxis
+set zzeroaxis
+set xlabel 'x, m'
+set ylabel 'y, m'
+set zlabel 'z, m'
+set output 'build/gnuplot/aurora.svg'
+splot 'ships/aurora.gnuplot'
diff --git a/gnuplot/cylinder.gnuplot b/gnuplot/cylinder.gnuplot
@@ -0,0 +1,22 @@
+set terminal svg dynamic size 1080/5, 1080/5 round enhanced font 'Liberation Sans, 10'
+#set key outside top center
+unset key
+set xtics -50,25,50 out nomirror offset 0,0.5
+set ytics -50,25,50 out nomirror offset 0.5,0
+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]
+set xlabel 'x, m' offset 0,1
+set ylabel 'y, m' offset 1,0
+set cblabel 'Velocity, m/s' offset -1,0
+s = 0.05
+set object 1 circle front at 0,0 size 54.8858/2 fillcolor rgb "black" lw 0.5
+set output "build/gnuplot/cylinder-1.svg"
+plot 'gnuplot/wind.orig' using 1:2:($3*s):($4*s):(sqrt($3**2+$4**2)) with vectors lw 0.1 lc palette
+set output "build/gnuplot/cylinder-2.svg"
+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/ship-roll-velocity.gnuplot b/gnuplot/ship-roll-velocity.gnuplot
@@ -0,0 +1,24 @@
+set terminal svg dynamic size 1080/6, 1080/6 round enhanced font 'Liberation Sans, 10'
+s = 180.0/pi
+#static_roll = 0.247885
+#static_roll = 0.246736
+static_roll = 0
+
+unset key
+set grid
+set border 1+2 back
+set xtics nomirror out offset 0,0.5
+set ytics nomirror out offset 0.5,0
+#set xrange [0:*]
+#set yrange [0:*]
+load 'gnuplot/rdbu.pal'
+
+set xlabel 'Wind velocity, m/s' offset 0,1
+set ylabel 'Roll angle, °' offset 1.5,0
+set output 'build/gnuplot/ship-roll.svg'
+plot 'gnuplot/wind-aurora.dat' using 1:($3*s) with linespoints ls 1 lw 2 pt 7 ps 0.5
+
+set ylabel 'Ship velocity, m/s'
+set output 'build/gnuplot/ship-velocity.svg'
+plot 'gnuplot/wind-aurora.dat' using 1:2 with linespoints ls 1 lw 2 pt 7 ps 0.5
+
diff --git a/slides.tex b/slides.tex
@@ -3,32 +3,301 @@
\setdefaultlanguage{english}
\usetheme{SaintPetersburg}
-\usepackage{textcomp}
\usepackage{booktabs}
+\usepackage{amsmath}
+\usepackage{spbu-tikz}
+
+\tikzset{Arrow/.style={
+ solid,
+ arrows={-Triangle[length=0.15cm,width=0.100cm]},
+ draw=spbuDarkGray
+}}%
+
+\tikzset{Dots/.style={
+ draw=spbuDarkGray,
+ line cap=round, dash pattern=on 0pt off 4\pgflinewidth
+}}%
+\setbeamertemplate{itemize items}[circle]
+
+% metadata
+\usepackage{textcomp}
+\usepackage{hyperxmp}
+\hypersetup{
+ pdfcontactemail={i.gankevich@spbu.ru},
+ pdfcontacturl={http://www.apmath.spbu.ru/en/staff/gankevich/index.html},
+ pdfcontactaddress={Unversitetskii prospekt 35},
+ pdfcontactcity={Petergof},
+ pdfcontactregion={Saint Petersburg},
+ pdfcontactpostcode={198504},
+ pdfcontactcountry={Russia},
+ pdflang={en},
+ pdfmetalang={en},
+ pdflicenseurl={http://creativecommons.org/licenses/by-sa/4.0/},
+ pdfcopyright={Copyright \textcopyright{} 2020 Anton Gavrikov\xmpcomma{} Alexander Degtyarev\xmpcomma{} Denis Egorov\xmpcomma{} Ivan Gankevich\xmpcomma{} Artemii Grigorev\xmpcomma{} Vasily Khramushin\xmpcomma{} Ivan Petriakov},
+ pdfsubject={Virtual Testbed: Simulation of air flow around ship hull and its effect
+on ship motions},
+}
+
+\newcommand{\VectorR}[1]{\left[\begin{array}{r}#1\end{array}\right]}
+\newcommand{\VectorL}[1]{\left[\begin{array}{l}#1\end{array}\right]}
+\newcommand{\Length}[1]{\big|#1\big|}
-\title{TODO}
+\title{Virtual Testbed: Simulation of air flow around ship hull and its effect
+on ship motions}
\author{%
A.\:Gavrikov \and
A.\:Degtyarev \and
D.\:Egorov \and
- I.\:Gankevich \and
+ I.\:Gankevich\textsuperscript{*} \and
A.\:Grigorev \and
V.\:Khramushin \and
I.\:Petriakov%
}
+\institute{Saint Petersburg State University}
\date{July 2020}
\begin{document}
\frame{\maketitle}
+\begin{frame}{Governing system of equations}
+ Continuity and motion equation for ideal fluid
+ \begin{columns}
+ \begin{column}{0.45\textwidth}
+ \begin{equation*}
+ \begin{aligned}
+ & \Delta\phi = 0; \qquad \vec\upsilon=\vec\nabla\phi; \\
+ & \rho\frac{\partial\phi}{\partial{}t} +
+ \frac{1}{2}\rho\Length{\vec\nabla\phi}^2 +
+ p + \rho g z = p_0
+ \end{aligned}
+ \end{equation*}
+ \end{column}
+ \begin{column}{0.45\textwidth}
+ \scriptsize
+ \begin{tabular}{ll}
+ \(p_0\) & atmospheric pressure \\
+ \(g\) & gravitational acceleration \\
+ \(\rho\) & air density \\
+ \(p\) & pressure \\
+ \(\phi\) & velocity potential \\
+ \(\vec\upsilon\) & velocity \\
+ \end{tabular}
+ \end{column}
+ \end{columns}
+ \vfill
+ Ship hull boundary condition
+ \begin{columns}
+ \begin{column}{0.45\textwidth}
+ \begin{equation*}
+ \vec\nabla\phi\cdot\vec{n} = 0;
+ \qquad
+ \vec{r} = \vec{S}
+ \end{equation*}
+ \end{column}
+ \begin{column}{0.45\textwidth}
+ \scriptsize
+ \begin{equation*}
+ \begin{aligned}
+ & \vec{r} = \left(x,y,z\right) \\
+ & \vec{S}=\vec{S}\left(a,b,t\right); \quad a,b\in{}A=[0,1];
+ \quad \vec{n}=\frac{\partial\vec S}{\partial a}\!\times\!\frac{\partial\vec S}{\partial b}
+ \end{aligned}
+ \end{equation*}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{The solution for uniform translational motion}
+ The law of reflection\newline
+ \vskip\baselineskip
+ \begin{center}
+ \begin{tikzpicture}[x=1mm,y=1mm]
+ \draw plot [smooth] coordinates
+ {(9.673,28.585) (17.173,35.433) (21.194,36.020) (27.064,35.433) (32.172,24.129)};
+ \node at (20,30) {\tiny{}ship hull};
+ \path[Arrow] (16.194,41.020) -- (21.194,36.020) {};
+ \draw[Dots] (11.194,46.020) -- (21.194,36.020) {};
+ \node[left] at (11.194,46.020) {\tiny{}incident air particle trajectory};
+ \node[left] at (16.194,41.020) {\(\vec\upsilon_{\phantom{r}}\)};
+ \path[Arrow] (21.194,36.020) -- (26.194,41.020) {};
+ \draw[Dots] (21.194,36.020) -- (31.194,46.020) {};
+ \node[right] at (31.194,46.020) {\tiny{}reflected air particle trajectory};
+ \node[right] at (26.194,41.020) {\(\vec\upsilon_r =
+ \vec\upsilon - 2\left(\vec\upsilon\cdot\vec{n}\right)\vec{n}\)};
+ \path[Arrow] (21.194,36.020) -- (21.194,41.020) {};
+ \node[above] at (21.194,41.020) {\(\vec{n}\)};
+ \end{tikzpicture}
+ \end{center}
+ \vfill
+ The solution \emph{on} the boundary
+ \begin{equation*}
+ \phi = \vec\upsilon\cdot\vec{r} + C \left(\vec\upsilon_r\cdot\vec{r}\right)
+ \qquad\Rightarrow\qquad
+ \vec\nabla\phi = \vec\upsilon + C\vec\upsilon_r =
+ \vec\upsilon + \vec\upsilon_r
+ \qquad
+ \text{\tiny{}(full derivation is in the paper)}
+ \end{equation*}
+ The solution \emph{near} the boundary
+ \begin{equation*}
+ \vec\nabla\phi =
+ \vec\upsilon +
+ \iint\limits_{a,b\,\in{}A}
+ \left(
+ \frac{1}{s} \vec\upsilon_r
+ - \frac{2}{s^2} \left(\vec\upsilon_r\cdot\vec{r}\right) \left(\vec{r}-\vec{S}\right)
+ \right)
+ da\,db;
+ \qquad
+ s = 1+\Length{\vec{r}-\vec{S}}^2.
+ \end{equation*}
+\end{frame}
+
+\begin{frame}{Verification using potential flow around a cylinder}
+ \centering
+ \begin{tikzpicture}[x=1cm,y=-1.2cm]
+ \node[text width=4.4cm,fill=spbuWhite2] (s1) at (0,0) {{\tiny{}Known solution in Cartesian form\strut{}}\newline \(\phi(x,y) = U x \left(1 + \frac{R^2}{x^2+y^2}\right)\)};
+ \node[text width=3.25cm,fill=spbuWhite2] (s2) at (8,0.5) {{\tiny{}Velocity on the boundary}\newline\(\vec\nabla\phi = \frac{2 U}{R^2}\VectorR{y^2 \\ -x y\phantom{^2}}\)};
+ \node[text width=4.4cm,fill=spbuWhite2] (s3) at (0,1) {{\tiny{}Our solution\strut{}}\newline\(\phi = \vec\upsilon\cdot\vec{r} + \vec\upsilon_r\cdot\vec{r}\)};
+ \node at (8,1.25) {\tiny{}(full derivation is in the paper)};
+ \path[Arrow] (s1.east) -- node[above]{\tiny{}\(x^2+y^2=R^2\)} (s1.east -| s2.west) ;
+ \path[Arrow] (s3.east) -- node[below]{\tiny{}\(\vec{n}=(x/R,y/R)\), \(\vec\upsilon=(U,0)\)} (s3.east -| s2.west) ;
+ \end{tikzpicture}
+ \vfill
+ \begin{columns}
+ \begin{column}{0.32\textwidth}
+ \centering
+ Known solution
+ \includegraphics{build/gnuplot/cylinder-1.eps}
+ \end{column}
+ \begin{column}{0.32\textwidth}
+ \centering
+ Our solution
+ \includegraphics{build/gnuplot/cylinder-2.eps}
+ \end{column}
+ \begin{column}{0.32\textwidth}
+ \footnotesize
+ \begin{itemize}
+ \item Two solutions are equivalent \emph{on} the boundary!
+ \item Max. difference near the boundary is 11\% of maximum velocity.
+ \end{itemize}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{Ship roll angle and velocity}
+ \begin{columns}
+ \begin{column}{0.25\textwidth}
+ \centering
+ Roll angle
+ \includegraphics{build/gnuplot/ship-roll.eps}
+ \end{column}
+ \begin{column}{0.25\textwidth}
+ \centering
+ Velocity
+ \includegraphics{build/gnuplot/ship-velocity.eps}
+ \end{column}
+ \begin{column}{0.45\textwidth}
+ \footnotesize
+ \begin{itemize}
+ \item
+ We need \(\approx{}35\) m/s wind (a hurricane!) to produce 1\textdegree{} static roll angle.
+ \item We need to introduce reflection ratio \(\alpha\) for symmetric ships:
+ \begin{equation*}
+ \vec\upsilon_r = \vec\upsilon -
+ 2 \alpha \left(\vec\upsilon\cdot\vec{n}\right)\vec{n}
+ \end{equation*}
+ \begin{tabular}{ll}
+ \(\alpha=0\) & no reflection \\
+ \(\alpha=1\) & full reflection \\
+ \end{tabular}
+ \end{itemize}
+ \includegraphics[scale=0.5]{build/gnuplot/aurora.eps}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{Performance benchmarks in Virtual Testbed}
+ \small
+ Average time in milliseconds that is needed to compute wind field on the
+ ship hull and near the ship hull.
+ \vfill
+ \begin{tabular}{l@{\hskip 3mm}r@{\hskip 2mm}r@{\hskip 3mm}r@{\hskip 2mm}r@{\hskip 3mm}r@{\hskip 2mm}rl}
+ \toprule
+ & \multicolumn{2}{c}{Diogen}
+ & \multicolumn{2}{c}{Aurora}
+ & \multicolumn{2}{c}{MICW} \\
+ \cmidrule(r){2-3}
+ \cmidrule(r){4-5}
+ \cmidrule(r){6-7}
+ Node & OpenMP & OpenCL
+ & OpenMP & OpenCL
+ & OpenMP & OpenCL \\
+ \midrule
+ Duck
+ & 114 & 14.00
+ & 164 & 16
+ & 314 & 29
+ & laptop
+ \\
+ GPUlab
+ & 62 & 1.35
+ & 90 & 2
+ & 175 & 3
+ & desktop
+ \\
+ Capybara & 33 & 0.87
+ & 48 & 1
+ & 99 & 6
+ & server
+ \\
+ \bottomrule
+ \end{tabular}
+ \vfill
+ \begin{tikzpicture}[x=1cm,y=1cm]
+ \node at (-4,0) {\includegraphics[scale=0.50]{build/ships/diogen.eps}};
+ \node at (0,0) {\includegraphics[scale=0.50]{build/ships/aurora.eps}};
+ \node at (4,0) {\includegraphics[scale=0.50]{build/ships/micw.eps}};
+ \end{tikzpicture}
+\end{frame}
+
+\begin{frame}{Conclusion and future work}
+ \begin{itemize}
+ \item The proposed solution is equivalent to the known
+ formula for potential flow around a cylinder.
+ \item High computational performance, especially on graphical accelerators.
+ \item Future work is to incorporate turbulence and circular motion into the model.
+ \end{itemize}
+\end{frame}
+
\begin{frame}
+ \centering
+ \begin{tabular}{lllrr}
+ \toprule
+ & & & \multicolumn{2}{c}{GPU GFLOPS} \\
+ \cmidrule(r){4-5}
+ Node & CPU & GPU & Single & Double \\
+ \midrule
+ Duck & Intel i7-3630QM & NVIDIA GT740M & 622 & \\
+ GPUlab & AMD FX-8370 & NVIDIA GTX1060 & 4375 & 137 \\
+ Capybara & Intel E5-2630 v4 & NVIDIA P5000 & 8873 & 277 \\
+ \bottomrule
+ \end{tabular}
+\end{frame}
+
+\begin{frame}
+ \vskip\baselineskip
+ \vskip\baselineskip
+ \vskip\baselineskip
+ \vskip\baselineskip
\tiny\vfill
- Copyright \textcopyright{} 2020 Ivan Petriakov
- \texttt{\href{mailto:st047437@student.spbu.ru}{st047437@student.spbu.ru}}. \\
+ Copyright \textcopyright{} 2020 Anton Gavrikov, Alexander Degtyarev, Denis
+ Egorov, Ivan Gankevich, Artemii Grigorev, Vasily Khramushin, Ivan Petriakov
+ \texttt{\href{mailto:i.gankevich@spbu.ru}{i.gankevich@spbu.ru}}. \\
\vskip\baselineskip
\vskip\baselineskip
- This work is licensed under a \alert{Creative Commons Attribution-ShareAlike 4.0
+ This work is licensed under a \textit{Creative Commons Attribution-ShareAlike 4.0
International License}. The copy of the license is available at
\url{https://creativecommons.org/licenses/by-sa/4.0/}.
\end{frame}
