A new absorbing layer for simulation of wave propagation based on a KdV model on unbounded domain

Abstract

Simulation for wave propagation based on the Korteweg-de Vries (KdV) equation on unbounded domain requires the computational domain to be bounded and hence an absorbing boundary condition is needed so that when the wave arrives the boundary it will not be reflected and destroy the simulation. In this article, we present a new absorbing (or called lossy) layer for simulation of wave propagation based on a KdV model on unbounded domain with non-homogeneous boundary condition at one end, and propose a two-level second-order accurate finite difference scheme for solving this KdV problem. We prove that both the analytical solution and the numerical solution are stable in L2-norm and l2-norm, respectively, and they decay in the lossy layer. Numerical examples are given to illustrate the new method and verify its effectiveness.