High-Resolution Lax-Friedrichs Scheme for Hyperbolic Conservation Laws withSource Terms: Application to Shallow Water Equations

摘要

A recently developed high resolution, non oscillatory staggered method, basedupon the Lax-Friedrichs scheme, for hyperbolic conservation laws, is considered. The staggered method is extended to include source terms, and it is also shown how to implement multiple dimensions. The advantage of using a staggered method is that Riemann problems no longer need to be solved. Numerical experiments are performed with the shallow water equations for which the staggered method yields sharp nonoscillatory shocks while retaining a high accuracy in regions where the flow is smooth. The accuracy obtained with the staggered method is significantly higher than in conventional finite difference schemes used in the field of meteorology.