MULTIDIMENSIONAL RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS

• 来源期刊: 计算数学（英文版）
• 关键词: Multidimensional hyperbolic systems Relaxation methods Non-oscillatory reconstructions Asymptotic-preserving schemes
• 年，卷（期）: 2007,（4）
• 页码范围: 440-457
• 页数: 18页
• 语种: 英文

摘要

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.