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An all Mach number relaxation upwind scheme. (English) Zbl 1447.65043
The authors deal with the low Mach number approximation of flows governed by the compressible Euler equations. They use the standard Suliciu relaxation technique and showed that it is not efficient for the approximation of these flow regimes. Instead, a modified relaxation scheme is constructed. It is shown that the numerical diffusion of the upwind scheme is controlled in the low Mach number case and that the relaxation scheme is robust. The asymptotic preserving property is also shown. Some numerical tests are given in 1D and 2D cases to demonstrate the performance of the modified relaxation scheme compared to a standard scheme.
MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q31 Euler equations
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