Numerical methods for nonconservative hyperbolic systems: a theoretical framework.

摘要: The goal of this paper is to provide a theoretical framework allowing one extend some general concepts related the numerical approximation 1-d conservation laws more case first order quasi-linear hyperbolic systems. In particular intended be useful for design and analysis well-balanced schemes solving balance or coupled systems laws. First, concept path-conservative introduced, which generalization conservative Then, we introduce definition approximate Riemann solvers give expression well-known families based on these solvers: Godunov, Roe, relaxation methods. Finally, form high scheme reconstruction operator presented.