A NUMERICAL METHOD FOR SPATIALLY NON-DECAYING CONSERVATION LAWS ON UNBOUNDED DOMAINS

Abstract

We discuss a numerical method for scalar conservation laws on multi dimensional unbounded domains. Since numerical approximations are made on a finite region, it is generally challenging to handle a solution that never diminishes on the open domain The presented scheme does not require an assumption that a solution decays to zero at infinity, which is different from conventional methods based on artificial boundary conditions. The algorithm is introduced from fixed-point iteration on implicit solutions that conservation laws possess. We can successfully reproduce shock formation occurring over open domain in nonlinear conservation laws. Several numerical results, including one and two dimensional Burgers' equations, are illustrated and compared to those from a conventional shock-handling method such as the WENO scheme.