154 research outputs found
Boussinesq Systems of Bona-Smith Type on Plane Domains: Theory and Numerical Analysis
We consider a class of Boussinesq systems of Bona-Smith type in two space
dimensions approximating surface wave flows modelled by the three-dimensional
Euler equations. We show that various initial-boundary-value problems for these
systems, posed on a bounded plane domain are well posed locally in time. In the
case of reflective boundary conditions, the systems are discretized by a
modified Galerkin method which is proved to converge in at an optimal
rate. Numerical experiments are presented with the aim of simulating
two-dimensional surface waves in complex plane domains with a variety of
initial and boundary conditions, and comparing numerical solutions of
Bona-Smith systems with analogous solutions of the BBM-BBM system
On Surface Waves in a Gibson Half-Space
Harmonic Rayleigh-type and transverse surface waves in a half-space of incompressible material with constant density and with shear modulus linearly increasing with depth (Gibson half-space) are discussed. Under certain hypotheses a discrete spectrum yielding polynomial Eigen functions is obtained, a fact which makes the eigenvalue problem more tractable. The dispersion laws are presented and evaluated numerically
A Finite Difference method for the Wide-Angle `Parabolic' equation in a waveguide with downsloping bottom
We consider the third-order wide-angle `parabolic' equation of underwater
acoustics in a cylindrically symmetric fluid medium over a bottom of
range-dependent bathymetry. It is known that the initial-boundary-value problem
for this equation may not be well posed in the case of (smooth) bottom profiles
of arbitrary shape if it is just posed e.g. with a homogeneous Dirichlet bottom
boundary condition. In this paper we concentrate on downsloping bottom profiles
and propose an additional boundary condition that yields a well posed problem,
in fact making it -conservative in the case of appropriate real
parameters. We solve the problem numerically by a Crank-Nicolson-type finite
difference scheme, which is proved to be unconditionally stable and
second-order accurate, and simulates accurately realistic underwater acoustic
problems.Comment: 2 figure
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