All Mach Number Second Order Semi-Implicit Scheme for the Euler Equations of Gasdynamics

摘要

This paper presents an asymptotic preserving (AP) all Mach number finitevolume shock capturing method for the numerical solution of compressible Eulerequations of gas dynamics. Both isentropic and full Euler equations areconsidered. The equations are discretized on a staggered grid. This simplifiesflux computation and guarantees a natural central discretization in the lowMach limit, thus dramatically reducing the excessive numerical diffusion ofupwind discretizations. Furthermore, second order accuracy in space isautomatically guaranteed. For the time discretization we adopt anSemi-IMplicit/EXplicit (S-IMEX) discretization getting an elliptic equation forthe pressure in the isentropic case and for the energy in the full Eulerequations. Such equations can be solved linearly so that we do not need anyiterative solver thus reducing computational cost. Second order in time isobtained by a suitable S-IMEX strategy taken from Boscarino et al. in [6].Moreover, the CFL stability condition is independent of the Mach number anddepends essentially on the fluid velocity. Numerical tests are displayed in oneand two dimensions to demonstrate performances of our scheme in bothcompressible and incompressible regimes.