Journal of Computational Physics
Journal of Computational Physics
Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed
Journal of Computational Physics
First- and second-order finite volume methods for the one-dimensional nonconservative Euler system
Journal of Computational Physics
Simulation of shallow-water systems using graphics processing units
Mathematics and Computers in Simulation
Short Note: A comment on the computation of non-conservative products
Journal of Computational Physics
HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
A Duality Method for Sediment Transport Based on a Modified Meyer-Peter & Müller Model
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Scientific Computing
A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems
Journal of Scientific Computing
Hyperconcentrated 1D Shallow Flows on Fixed Bed with Geometrical Source Term Due to a Bottom Step
Journal of Scientific Computing
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System
Journal of Scientific Computing
Journal of Computational Physics
A multilayer shallow water system for polydisperse sedimentation
Journal of Computational Physics
Journal of Computational Physics
A diffuse interface model with immiscibility preservation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes
Journal of Computational Physics
Hi-index | 0.07 |
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.