commit 7329263a308252e474feba4b90e849768bfa89dd
parent b477807a014b102498ad39a76f00d569b6f270e0
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Tue, 30 Jun 2020 13:37:51 +0300
Talk.
Diffstat:
| Makefile | | | 47 | ++++++++++++++++++++++------------------------- |
| talk.org | | | 115 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
2 files changed, 137 insertions(+), 25 deletions(-)
diff --git a/Makefile b/Makefile
@@ -8,36 +8,33 @@ FLAGS = \
-bibtex \
-shell-escape
-NAME = iccsa-20-waves
-SLIDES = slides
-
-all: build/$(NAME).pdf
-all: build/$(SLIDES).pdf
+all: build/main.pdf
+all: build/slides.pdf
all: build/287-Gankevich-Ocean-wave-reflection.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
-build/$(NAME).pdf: main.tex
-build/$(NAME).pdf:
+build/main.pdf: build/gnuplot/openmp.svg
+build/main.pdf: build/gnuplot/surface.eps
+build/main.pdf: build/gnuplot/surface.svg
+build/main.pdf: build/ships/aurora.eps
+build/main.pdf: build/ships/diogen.eps
+build/main.pdf: build/ships/micw.eps
+build/main.pdf: main.tex
+build/main.pdf:
@echo " LATEX $<"
@-$(LATEXMK) $(FLAGS) -f main.tex
-build/$(SLIDES).pdf: build/gnuplot/openmp.svg
-build/$(SLIDES).pdf: build/gnuplot/aurora.eps
-build/$(SLIDES).pdf: build/gnuplot/aurora-non-bare.eps
-build/$(SLIDES).pdf: build/gnuplot/diogen.eps
-build/$(SLIDES).pdf: build/gnuplot/micw.eps
-build/$(SLIDES).pdf: build/gnuplot/surface-with-ship.eps
-build/$(SLIDES).pdf: build/gnuplot/surface-with-ship-3d.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: build/inkscape/diffraction.eps
-build/$(SLIDES).pdf: slides.tex
+build/slides.pdf: build/gnuplot/openmp.svg
+build/slides.pdf: build/gnuplot/aurora.eps
+build/slides.pdf: build/gnuplot/aurora-non-bare.eps
+build/slides.pdf: build/gnuplot/diogen.eps
+build/slides.pdf: build/gnuplot/micw.eps
+build/slides.pdf: build/gnuplot/surface-with-ship.eps
+build/slides.pdf: build/gnuplot/surface-with-ship-3d.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: build/inkscape/diffraction.eps
+build/slides.pdf: slides.tex
@echo " LATEX $<"
@-$(LATEXMK) $(FLAGS) -xelatex -f $<
diff --git a/talk.org b/talk.org
@@ -0,0 +1,115 @@
+* Slide 1
+
+My next talk is about ocean wave reflection from the ship hull. In this talk we
+again apply the law of reflection to simulate diffraction of the waves near the
+ship hull.
+
+* Slide 2
+
+The initial goal of this work was to replace empirical methods (namely, the
+method of added masses) currently used in ship motions simulators to model ship
+resistance to flow with diffraction and radiation. But in the course of the
+experiments we changed the goal to just simulation of diffraction: it is too
+early to talk about replacement of the method of added masses. We need more time
+to understand and simulate every physical phenomena that contributes to ship
+resistance to flow. In this talk I will present only wave /diffraction/
+
+* Slide 3
+
+Wave diffraction is the change of wave direction due to obstacles: when a wave
+meets obstacle (like an island or a ship) it slowly changes its direction to be
+tangent to the boundary of the obstacle. There are three regions associated with
+the diffraction:
+- in the first region the wave slows down before approaching the
+ obstacle,
+- in the second region the wave goes around the obstacle and its direction becomes
+ tangent to the boundary, and
+- in the third region waves that went around different sides of the obstacle interfere
+ with each other.
+The solution used in this work simulates only the first and the second region.
+The third region is simulated the same way as the first one, but the wave
+increases its speed instead of slowing down.
+
+To simulate the change of wave direction due to diffraction we use the law of reflection.
+Informally, the law of reflection states that
+- the incident ray, the reflected ray and the surface normal lie in the same plane and
+- the angle of incidence equals the angle of reflection.
+We use it for ocean waves instead of light rays. This approach can also be found in the
+literature.
+
+We describe incident wave direction as the vector of wave numbers third
+component of which is nought (because we consider surface waves, not spherical
+ones). Reflected wave direction vector is derived using basic geometric
+principles (you can see the formula on the slide). On order to write potentials
+using vector notation we introduce pseudo-vector \(\vec{d}_k\) that contains
+decay coefficient. The potential has the usual form of complex exponent, in
+order to get the real potential we need to take double real part of the
+exponent. Then the total potential is written as weighted sum of the potentials
+for incident and reflected wave and it is the form of the solution that we seek
+in this problem.
+
+* Slide 4
+
+The governing system of equations for potential flow includes
+- equation of continuity (that describes conservation of mass),
+- equation of motion (that describes conservation of momentum) and
+- boundary condition on the ship hull (that nullifies water velocity on the
+ boundary).
+The ship hull is defined by the collection of triangular panels each of which
+has the normal \(\vec{n}\) and the point \(\vec\zeta_0\) that lies in the plane
+of the panel.
+
+The solution /on/ the boundary, where neighbouring panels do not affect each
+other, has simple form with \(C_1=1\) and \(C_2\) being equal to some exponent.
+The solution /near/ the boundary, where all panels contribute to the velocity
+potential is constructed using smoothing kernel (similar to air flow from the
+previous talk). We compute weighted sum of reflected wave potentials for all
+panels, the potential decays quadratically with the distance to the panel. So,
+the solution on the boundary is precise, and the solution near the boundary is
+just a weighted sum that happens to satisfy all equations in the system. For
+the purpose of simulating ship motions we need only the solution on the
+boundary.
+
+* Slide 5
+
+We simulated diffraction around Aurora's ship hull. In the picture we can see
+that waves near the hull have more pronounced crests and troughs (i.e. slightly
+larger amplitude). We can clearly see the first region where the wave slows
+down, and the second region where the wave direction follows ship waterline (it
+is more visible with huge cylinder: the ship is too small compared to the island
+to substantially change the direction of the wave). So, our solution correctly
+simulates wave diffraction.
+
+* Slide 6
+
+Here is the same picture in three dimensions and without the ship. In greyscale
+the change in amplitude is more visible.
+
+* Slide 7
+
+Finally, we benchmarked our solution on CPU and GPU using three ships with
+different number of panels and three computers with different performance
+characteristics. In this work we used local memory to optimised handling of
+large number of panels in GPU kernel. As you can see from the table, this
+optimisation allowed us to get much larger speedups than in air flow simulation.
+In the best case GPU performance is three orders of magnitude higher than CPU
+performance.
+
+* Slide 8
+
+Although, our solution for wave diffraction near ship hull works, it can not
+replace the method of added masses. We can not use it compute ship resistance to
+flow. The future work is to simulate wave radiation and check if it can be used
+to compute ship resistance to flow. And if it is not we have to resort to
+viscous flows near the ship hull, which is a different and much more difficult
+problem compared to diffraction and radiation.
+
+To summarise the two talks, the law of reflection can be successfully applied
+not only to light ray reflection but also for ocean wave reflection and air
+particle reflection from the boundary. In case of air flow the solution you
+obtain using law of reflection is equivalent to the known solution for potential
+flow around a cylinder, in case of ocean waves it is not equivalent but close to
+the solution from linear wave theory (I did not show this in the paper). The
+advantage of the law of reflection-based solutions is that they can be easily
+generalised to the object of any form using smoothing kernel with quadratic
+decay.
