Numerics for Hyperbolic Conservation Laws with Help from the Physical Entropy

Abstract

Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an additional equation to eliminate the numerically critical terms with simple substitutions. The method has potential for a wider applicability than the particular example presented here.

12 pages, 3 figures

References in corpus (2)

• Hilbert's 6th Problem: Exact and Approximate Hydrodynamic Manifolds for Kinetic Equations
• Entropic 13 Moment Equations from Boltzmann's Kinetic Equation

Cited by in corpus (2)

• Thermodynamical extension of a symplectic numerical scheme with half space and time shift demonstrated on rheological waves in solids
• Four spacetime dimensional simulation of rheological waves in solids and the merits of thermodynamics