The dominant wave-capturing flux: A finite-volume scheme without decomposition for systems of hyperbolic conservation laws

DOI10.1016/j.jcp.2006.02.005zbMath1103.65093OpenAlexW2000582480MaRDI QIDQ853186

Michael G. Edwards

Publication date: 15 November 2006

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2006.02.005

zbMATH Keywords

numerical exampleshyperbolic systemsLax-Friedrichs fluxfinite-volume methoddominant waveRusanov flux

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (6)

On a modification of the Rusanov solver for the equations of special relativistic magnetic hydrodynamics ⋮ Efficient dissipation-based nonlinear solver for multiphase flow in discrete fractured media ⋮ Simulation of multiphase flows in porous media with gravitational effects using dominant wave method ⋮ A new Rusanov-type solver with a local linear solution reconstruction for numerical modeling of white dwarf mergers by means massive parallel supercomputers ⋮ Accurate particle splitting for smoothed particle hydrodynamics in shallow water with shock capturing ⋮ Global and local central non-upwind finite volume schemes for hyperbolic conservation laws in porous media

Cites Work

• Unnamed Item
• Unnamed Item
• Non-oscillatory central differencing for hyperbolic conservation laws
• Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
• Construction of explicit and implicit symmetric TVD schemes and their applications
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• A class of implicit upwind schemes for Euler simulations with unstructured meshes
• Approximate Riemann solvers, parameter vectors, and difference schemes
• On central-difference and upwind schemes
• A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
• The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case
• A review and comparative study of upwind biased schemes for compressible flow computation. III: Multidimensional extension on unstructured grids.
• Positive schemes for solving multi-dimensional hyperbolic systems of conservation laws. II
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• The solution of non-linear hyperbolic equation systems by the finite element method
• High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
• A Multiple-Grid Scheme for Solving the Euler Equations
• A second-order accurate, component-wise TVD scheme for nonlinear, hyperbolic conservation laws

This page was built for publication: The dominant wave-capturing flux: A finite-volume scheme without decomposition for systems of hyperbolic conservation laws