commit 7c09169adb688f0e7794f72ebdcab55f3d00ba90
parent f5f86af80cd925e0b2089c3c906b18b1a192151d
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Thu, 18 Apr 2019 15:03:12 +0300
Make it short and structured.
Diffstat:
| main.tex | | | 68 | ++++++++++++++++++++++++++------------------------------------------ |
1 file changed, 26 insertions(+), 42 deletions(-)
diff --git a/main.tex b/main.tex
@@ -27,50 +27,34 @@
% Full text of abstract. If you use some graphics, don't forget to send it together with abstract.
\mmcpAbstract{%
-Direct numerical experiments in ship hydromechanics involve non-stationary
-interaction of a ship hull and intensive threedimensional wavy surface that
-include formation of vortices, surfaces of jet discontinuities, and
-discontinuities in fluid under influence of negative pressure in particular.
-Unique physical phenomena occur not only in close vicinity to ship hull
-fragments, but also at a distance to the ship where waves break as a result of
-interference of sea and ship waves. To simulate these phenomena we use
-analytic, computational and empirical models simultaneously to adapt
-computations based on instantaneous evaluations of local spatial regions.
-
-Explicit numerical schemes simulate propagation of large-amplitude sea waves
-and their transformations after the impact with a ship or a stationary
-structure. This problem reduces to determining wave kinematics on a moving
-boundary of a ship hull and a free boundary of a computational domain.
-
-In wave equation in place of velocity field we integrate streams of fluid
-represented by functions as smooth as wavy surface elevation field. We assume
-that within boundaries of computational domain waves do not disperse,
-i.e.~their length and period stays the same. Under this assumption we simulate
-trochoidal Gerstner waves \mcite{gerstner} of a particular period. Gerstner
-waves satisfy continuity equation and in fact are the only exact solution of
-equations describing propagation of gravitational waves on the surface of a
-fluid. Wavy surface boundary have to satisfy Bernoulli equation: pressure on
-the surface of the wave becomes non-constant, fluid particles drift in the
-upper layers of a fluid in the direction of wave propagation~\mcite{shuleikin},
-and vortices form as a result.
-
-We build a grid of large particles having a form of a parallelepiped (tensors
-basis). As the depth increases, kinetic energy descreases exponentially which
-leads to decrease of total speed of wave energy propagation. This is feasible
-only as a compensation of reflection of upper fluid layers, i.e.~continuous
-change of a wave front phase and accompanying interference of waves propagating
-in opposite directions with a small change in frequency. As a result, ``ninth
-waves'', a standing wave with much larger significat wave height, form on the
-wavy surface.
-
-Trochoidal wave theory uses Lagrange coordinates which are naturally described
-physically by large particles and mathematically by tensors. Fluid particles
-drift in the upper layers of a fluid is simulated by changing curvatures of
-particles trajectories based on the instantaneous change of wavy surface
-elevation. So, the model includes unsteady hydromechanics.
+Numerical experiments in ship hydromechanics involve non-stationary interaction
+of a ship hull and wavy surface that include formation of vortices, surfaces of
+jet discontinuities, and discontinuities in fluid under influence of negative
+pressure. These physical phenomena occur not only near ship hull, but also at
+a distance where waves break as a result of interference of sea waves and waves
+reflected from the hull.
In the study reported here we simulate wave breaking and reflection near the
-ship hull.
+ship hull. We use explicit numerical schemes to simulate propagation of
+large-amplitude sea waves and their transformation after the impact with a
+ship. The problem reduces to determining wave kinematics on a moving boundary
+of a ship hull and a free boundary of a computational domain. We build a grid
+of large particles having a form of a parallelepiped, and in wave equation in
+place of velocity field we integrate streams of fluid represented by functions
+as smooth as wavy surface elevation field. We assume that within boundaries of
+computational domain waves do not disperse, i.e.~their length and period stays
+the same. Under this assumption we simulate trochoidal Gerstner
+waves~\mcite{gerstner} of a particular period. Wavy surface boundary have to
+satisfy Bernoulli equation: pressure on the surface of the wave becomes
+non-constant, fluid particles drift in the upper layers of a fluid in the
+direction of wave propagation~\mcite{shuleikin}, and vortices form as a result.
+The drift is simulated by changing curvatures of particles trajectories based
+on the instantaneous change of wavy surface elevation.
+
+This approach allows to simulate wave breaking and reflection near ship hull.
+The goal of the research is to develop a new method of taking wave reflection
+into account in ship motion simulations as an alternative to the classic method
+that uses added masses.
}
