Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/050628052 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
order path-conservative scheme,general definition,general concept,numerical method,general form,theoretical framework,nonconservative hyperbolic system,conservation law,numerical approximation,general expression,1-d conservation law,general case,high order scheme,relaxation methods,finite volume method | Applied mathematics,Mathematical optimization,Linear system,Relaxation (iterative method),Godunov's scheme,Operator (computer programming),Numerical analysis,Finite volume method,Mathematics,Conservation law,Calculus,Numerical linear algebra | Journal |
Volume | Issue | ISSN |
44 | 1 | 0036-1429 |
Citations | PageRank | References |
76 | 5.48 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carlos Parés | 1 | 353 | 35.30 |