Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws
SIAM Journal on Scientific Computing
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
A relaxation method for two-phase flow models with hydrodynamic closure law
Numerische Mathematik
MUSTA Fluxes for systems of conservation laws
Journal of Computational Physics
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In this work we establish conditions for an approximate simple Riemann solver to satisfy a semi-discrete entropy inequality. The semi-discrete approach is less restrictive than the fully-discrete case and allows to grant some other good properties for numerical schemes. First, conditions are established in an abstract framework for simple Riemann solvers to satisfy a semi-discrete entropy inequality and then the results are applied, as a particular case, to the Suliciu system. This will lead in particular to the definition of schemes for the isentropic gas dynamics and the full gas dynamics system that are stable and preserve the stationary shocks.