OPERATOR-SPLITTING-BASED ASYMPTOTIC PRESERVING SCHEME FOR THE GAS DYNAMICS EQUATIONS WITH STIFF SOURCE TERMS

摘要

We propose a numerical scheme for the gas dynamics equations with external forces and friction terms that is able to accurately approximate the flow in the large friction regime with a coarse spatial discretization. The key idea is to use a classic convection/source operator splitting and then to reduce the numerical diffusion involved with the approximation of the convective terms when the friction effects are dominant. The overall resulting scheme satisfies a discrete entropy inequality under a condition on the numerical diffusion reduction. Numerical tests are proposed in 1D and 2D that show a gain of accuracy.