A nonlinear flux split method for hyperbolic conservation laws

Authors:
Youssef Stiriba
Affiliations:
CERFACS/CFD Team, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France
Venue:
Journal of Computational Physics
Year:
2002

Citing 14
Cited 0

Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux

Journal of Computational Physics
Simplified second-order Godunov-type methods

SIAM Journal on Scientific and Statistical Computing
An approximate linearised Riemann solver for the Euler equations for real gases

Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II

Journal of Computational Physics
Splitting of inviscid fluxes for real gases

Journal of Computational Physics
The behavior of flux difference splitting schemes near slowly moving shock waves

Journal of Computational Physics
On Godunov-type methods near low densities

Journal of Computational Physics
Sonic flux formulae

SIAM Journal on Scientific and Statistical Computing
Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws

SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes

Journal of Computational Physics
Efficient implementation of weighted ENO schemes

Journal of Computational Physics
Capturing shock reflections: an improved flux formula

Journal of Computational Physics
On postshock oscillations due to shock capturing schemes in unsteady flows

Journal of Computational Physics
An isobaric fix for the overheating problem in multimaterial compressible flows

Journal of Computational Physics

Quantified Score

Hi-index	31.45

Visualization

Abstract

We present and analyze the performance of a nonlinear, upwind flux split method for approximating solutions of hyperbolic conservation laws. The method is based on a new version of the single-state-approximate Riemann solver devised by Harten, Lax, and van Leer (HLL) and implemented by Einfeldt. It makes use of two-sided local characteristic variables to reduce the dissipation of HLL by introducing the flavor of HLL into the Steger--Warming flux vector splitting scheme. We use the characteristic decomposition and the method-of-lines approach to construct high-order versions of the first-order scheme and demonstrate their efficiency and robustness in several numerical tests.