commit 92406835577707097f4e498e269ad0d76303ee09 parent 0e60291d685dbf32840d9422c4a53f771ac7d1d4 Author: Ivan Gankevich <i.gankevich@spbu.ru> Date: Mon, 27 Apr 2020 13:14:43 +0300 Results for diffraction. Diffstat:
| Makefile | | | 2 | ++ |
| data/surface-diffraction-aurora.dat | | | 10000 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| data/surface-diffraction.dat | | | 10000 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| data/surface.dat | | | 10000 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| gnuplot/surface.gnuplot | | | 21 | +++++++++++++++++++++ |
| main.tex | | | 71 | ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++------------- |
6 files changed, 30081 insertions(+), 13 deletions(-)
diff --git a/Makefile b/Makefile @@ -15,6 +15,8 @@ all: build/$(NAME).pdf all: build/$(SLIDES).pdf build/$(NAME).pdf: build/gnuplot/openmp.svg +build/$(NAME).pdf: build/gnuplot/surface.eps +build/$(NAME).pdf: build/gnuplot/surface.svg build/$(NAME).pdf: build/ships/aurora.eps build/$(NAME).pdf: build/ships/diogen.eps build/$(NAME).pdf: build/ships/micw.eps diff --git a/data/surface-diffraction-aurora.dat b/data/surface-diffraction-aurora.dat @@ -0,0 +1,10000 @@ +-100.085 -99.9917 -0.48264 +-100.084 -97.9711 -0.465543 +-100.084 -95.9507 -0.447803 +-100.085 -93.9303 -0.429606 +-100.085 -91.9101 -0.41116 +-100.087 -89.8899 -0.392691 +-100.088 -87.8699 -0.374443 +-100.09 -85.8501 -0.356673 +-100.092 -83.8303 -0.339651 +-100.094 -81.8107 -0.323652 +-100.097 -79.7913 -0.308963 +-100.1 -77.772 -0.295863 +-100.103 -75.7528 -0.284635 +-100.106 -73.7338 -0.275552 +-100.11 -71.7149 -0.268878 +-100.113 -69.6961 -0.264861 +-100.117 -67.6775 -0.263731 +-100.12 -65.6589 -0.265697 +-100.124 -63.6404 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-0.465647 +99.861 73.7374 -0.465647 +99.861 75.7576 -0.465647 +99.861 77.7778 -0.465647 +99.861 79.798 -0.465647 +99.861 81.8182 -0.465647 +99.861 83.8384 -0.465647 +99.861 85.8586 -0.465647 +99.861 87.8788 -0.465647 +99.861 89.899 -0.465647 +99.861 91.9192 -0.465647 +99.861 93.9394 -0.465647 +99.861 95.9596 -0.465647 +99.861 97.9798 -0.465647 +99.861 100 -0.465647 diff --git a/gnuplot/surface.gnuplot b/gnuplot/surface.gnuplot @@ -0,0 +1,21 @@ +set terminal svg size 1920/3,1080/3 dynamic +#set hidden3d back offset 0 trianglepattern 3 undefined 1 altdiagonal bentover +set view equal xyz +#set view ,,4 +set view map +set xrange [-100:100] +set yrange [-100:100] +set cbrange [-2:2] +set cbtics -2,0.5,2 +set palette defined (0 '#404040', 1 '#fffff0', 2 '#0040f0') +unset key +unset xtics +unset ytics +unset ztics +unset border +set pm3d +set style data pm3d +set dgrid3d 200,200 exp +set output 'build/gnuplot/surface.svg' +#splot 'data/surface.dat' with pm3d +splot 'data/surface-diffraction-aurora.dat' with pm3d diff --git a/main.tex b/main.tex @@ -3,6 +3,7 @@ \usepackage{amsmath} \usepackage{amssymb} \usepackage{booktabs} +\usepackage{cite} \usepackage{graphicx} \usepackage{url} @@ -221,7 +222,7 @@ solutions will be studied in future work. \subsection{Stationary surface boundary} In this section we explore solutions stationary surface boundary in a form of -infinite plain surface. On such a boundary the projection of particle velocity +infinite plane surface. On such a boundary the projection of particle velocity to the surface normal is nought. We write boundary conditions and corresponding solutions for different orientations of this boundary and then generalise these solutions to a parametric surface. @@ -363,11 +364,11 @@ component of the normal vector is nought: \(\vec{n}=(n_1,n_2,0)\), The direction of incident wave is \(\vec{d}_i=(u,v,0)\) and the direction of reflected wave is \(\vec{d}_r\). We seek solutions of the form \begin{equation} -\label{eq-w-all-0} +\label{eq-solution-diffraction} \begin{aligned} -w\left(\alpha,\beta,\delta,t\right) = & +w\left(\alpha,\beta,\delta,t\right) = &\: C_1\exp\left( \left(i\vec{d}_i+\vec{d}_{k}\right)\cdot\vec\zeta - i\omega_1 -t\right) \\ + & +t\right) \\ + &\: C_2\exp\left( \left(i\vec{d}_r+\vec{d}_{k}\right)\cdot\vec\zeta - i\omega_2 t\right). \end{aligned} \end{equation} @@ -389,9 +390,16 @@ Hence and \(C_2=\frac{1}{2}\exp\left(\frac{1}{2}i\vec{d}_s\cdot\vec\zeta_0\right)\). This solution reduces to the solution for the wall when \(\vec{n}=(0,0,1)\). +In a computer programme it is more practical to set \(C_1=1\) and +\(C_2=\exp\left(i\vec{d}_s\cdot\zeta_0\right)\): that way you have to integrate +only the second term in the solution over all ship hull panels +(see~sec.~\ref{sec-results-diffraction}). + %\input{stationary-surface.tex} %\input{progressively-moving-surface.tex} +%\subsection{Non-stationary surface boundary} + \subsection{OpenCL implementation} Solution for fluid velocity field was implemented in velocity potential solver @@ -459,6 +467,38 @@ Following these simple rules, we can easily implement efficient algorithms. \section{Results} +\subsection{Diffraction} +\label{sec-results-diffraction} + +In the first experiment we use solution for infinite panel to simulate wave +diffraction around Aurora's ship hull (see~fig.~\ref{fig-ships}). In order to +apply~\eqref{eq-solution-diffraction} to this problem we use smoothing kernel +that accumulates influence of every panel on a particular point of ocean +surface: +\begin{equation*} + w = \sum\limits_{j} K_j w_j; + \qquad + K_j = \frac{1}{1 + \left|\zeta-\zeta_0\right|^2} +\end{equation*} +Here \(w_j\) is solution~\eqref{eq-solution-diffraction} written for panel +\(j\), \(K_j\) is smoothing kernel, \(\zeta_0\) is the centre of the panel. +In the centre of the panel \(K_j=0\) and far from the ship hull +\(K_j\rightarrow{}0\). + +In the experiment waves with amplitude 1 approach the ship from the aft. The +results of the experiment are shown in fig.~\ref{fig-diffraction}. Near the +aft waves changes theire direction to be tangent to the waterline curve, follow +the curve all the way to the bow, and then restore their original direction. +The amplitude of waves near the hull is also increased. + +\begin{figure} + \centering + \includegraphics{build/gnuplot/surface.eps} + \caption{Wave diffraction around Aurora's hull (the hull is not + shown).\label{fig-diffraction}} +\end{figure} + + \subsection{Performance benchmarks} We implemented velocity potential solver using OpenMP for parallel computations @@ -534,20 +574,25 @@ processor (tab.~\ref{tab-config}). \section{Discussion} All the solutions obtained for various boundaries satisfy continuity equation -and equation of motion, but they are all written for plain surface boundary +and equation of motion, but they are all written for plane surface boundary with different orientations. Typical ship hull three-dimensional model is represented by triangulated surface, and in the centre of each panel fluid particle velocity vector does not depend on the surface normal of the panel and -not other panels. So, the solution for plain surface boundary is enough to +not other panels. So, the solution for plane surface boundary is enough to compute fluid velocity field directly \emph{on} the surface boundary. In order to generalise the solution fluid velocity field \emph{near} the surface boundary, we need to calculate weighted average of reflection terms of -each underwater panel of the surface. Our preliminary tests showed that simple -average is enough to visualise waves reflecting from the hull, but the approach -that uses signed panel area or signed tetrahedron volume to account for -direction of the surface normal relative to wave direction may give more -accurate results. +each underwater panel of the surface. Using inverse squared distance as the +weight gives acceptable results in our experiments, but may not be appropriate +in others. + +It is not clear how much we have to increase wave amplitude near the boundary. +One way to control the amptlitude increase is to introduce the coefficient +\(C\) into the reflection formula \(\vec{d}_r=\vec{d}_i-C\vec{d}_s\) and before +reflection term in~\eqref{eq-solution-diffraction}. When \(C=1\) the wave is +fully reflected from the boundary and the amplitude is doubled, when \(C=0\) no +reflection occurres and the amplitude does not change. Performance benchmarks showed that graphical accelerator greatly improves performance of velocity potential solver. Linear memory access patterns and @@ -559,10 +604,10 @@ deriving explicit solution for fluid motions near the ship hull boundary. This paper proposes a new model for ocean wave diffraction near ship hull. This model uses law of reflection to simulate incident and reflected waves and -fluid particle motion. Although, the solutions are written for infinite plain +fluid particle motion. Although, the solutions are written for infinite plane surfaces, they can be used to compute fluid velocity at the centre of each triangle of the triangulated ship hull surface and can be generalised to -compute fluid velocity near the ship hull uses weighted sum over all panels. +compute fluid velocity near the ship hull using weighted sum over all panels. The model was implemented in Virtual testbed velocity potential solver and was found to be highly efficient on a graphical accelerator. Future work is to