Radiation Boundary Conditions for the Two - Dimensional Wave Equation from a Variational Principle Jan
نویسندگان
چکیده
A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon. In an accompanying paper the underlying theory is presented.
منابع مشابه
Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves
The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...
متن کاملVariational Principle and Plane Wave Propagation in Thermoelastic Medium with Double Porosity Under Lord-Shulman Theory
The present study is concerned with the variational principle and plane wave propagation in double porous thermoelastic infinite medium. Lord-Shulman theory [2] of thermoelasticity with one relaxation time has been used to investigate the problem. It is found that for two dimensional model, there exists four coupled longitudinal waves namely longitudinal wave (P), longitudinal thermal wave (T),...
متن کاملRayleigh Wave in an Incompressible Fibre-Reinforced Elastic Solid Half-Space
In this paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function. The general solution of the equation of motion is obtained, which satisfies the required radiation condition. The appropriate traction free boundary conditions are also satisfied by the solution to obtain the required secular equation for...
متن کاملSolution of Wave Equations Near Seawalls by Finite Element Method
A 2D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve non...
متن کاملA High Order Approximation of the Two Dimensional Acoustic Wave Equation with Discontinuous Coefficients
This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditio...
متن کامل