Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
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DOI：
10.1137/050628052
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发表时间：
2006-01
影响因子：
2.9
通讯作者：
C. Parés
中科院分区：
文献类型：
--
作者：
C. Parés
本文的目标是提供一个理论框架，允许一个扩展到更一般的情况下，一阶拟线性双曲方程组的1-D守恒律的数值逼近的一些一般概念。特别是这个框架的目的是有用的设计和分析以及平衡的数值方案，解决平衡法或耦合系统的守恒律。首先，引入了路径守恒数值格式的概念，它是守恒律方程组守恒格式概念的推广。然后，我们介绍了近似Riemann解的一般定义，并给出了一些著名的家庭计划基于这些解：Goddom，Roe和松弛方法的一般表达式。最后给出了基于一阶路径守恒格式和重构算子的高阶格式的一般形式。
The goal of this paper is to provide a theoretical framework allowing one to extend some general concepts related to the numerical approximation of 1-d conservation laws to the more general case of first order quasi-linear hyperbolic systems. In particular this framework is intended to be useful for the design and analysis of well-balanced numerical schemes for solving balance laws or coupled systems of conservation laws. First, the concept of path-conservative numerical schemes is introduced, which is a generalization of the concept of conservative schemes for systems of conservation laws. Then, we introduce the general definition of approximate Riemann solvers and give the general expression of some well-known families of schemes based on these solvers: Godunov, Roe, and relaxation methods. Finally, the general form of a high order scheme based on a first order path-conservative scheme and a reconstruction operator is presented.