Multidimensional Relaxation Approximations for Hyperbolic Systems of Conservation Laws

Authors

  • Mohammed Seaïd Universit¨at Kaiserslautern Fachbereich Mathematik, 67663 Kaiserslautern, Germany

Keywords:

Multidimensional hyperbolic systems, Relaxation methods, Non-oscillatory reconstructions, Asymptotic-preserving schemes.

Abstract

We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations. To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.

Published

2007-08-02

Issue

Section

Articles