High order nite-di erence approximations of the wave equation with absorbing boundary conditions: a stability analysis
نویسنده
چکیده
This paper deals with the stability of nite di erence approximations of initial value problems for the wave equation with absorbing boundary conditions. The stability of a family of high order variational numerical schemes is studied by energy techniques. Dirichlet, sponge and rst order paraxial absorbing boundary conditions are treated. The variational form of the schemes as well as the use of the image principle are essential for the discrete energy estimates. With these estimates conditional stability is shown to be equivalent to the positivity of the kinetic energy operator. The main result of the paper is to show how to couple the discretization of the equation in the interior to the discretization of the boundary condition for a particular class of schemes.
منابع مشابه
PhysicsUpwind Compact and Explicit High - Order Finite Di erenceSchemes for Direct Numerical Simulation of High - Speed
Direct numerical simulation of transitional and turbulent hypersonic boundary layers using the Navier-Stokes equations requires high-order accurate numerical methods to resolve a wide range of time and length scales. Compact or explicit nite di erence methods used for such simulation have mainly been central di erence schemes containing only phase errors without any numerical dissipation. Centr...
متن کاملNumerical Absorbing Boundary Conditions for the Wave Equation
We develop a theory of difference approximations to absorbing boundary conditions for the scalar wave equation in several space dimensions. This generalizes the work of the author described in [8]. The theory is based on a representation of analytical absorbing boundary conditions proven in [8]. These conditions are defined by compositions of first-order, one-dimensional differential operators....
متن کاملOrr Sommerfeld Solver Using Mapped Finite Di?erence Scheme for Plane Wake Flow
Linear stability analysis of the three dimensional plane wake flow is performed using a mapped finite di?erence scheme in a domain which is doubly infinite in the cross–stream direction of wake flow. The physical domain in cross–stream direction is mapped to the computational domain using a cotangent mapping of the form y = ?cot(??). The Squire transformation [2], proposed by Squire, is also us...
متن کاملFinite Volume Methods for Convection Diffusion Problems
Introduction In this paper we consider cell centered nite di erence approximations for second order convection di usion equations of divergence type Our goal is to construct nite di erence methods of second order of approximation that satisfy the discrete maximum principle The error estimates are in the discrete Sobolev spaces associated with the considered boundary value problem Approximation ...
متن کاملStability of wide-angle absorbing boundary conditions for the wave equation
Numerical solution of the two-dimensional wave equation requires mapping from a physical domain without boundaries to a computational domain with artificial boundaries. For realistic solutions, the artificial boundaries should cause waves to pass directly through and thus mimic total absorption of energy. An artificial boundary which propagates waves in one direction only is derived from approx...
متن کامل