A Mach-Sensitive Implicit-Explicit Scheme Adapted to Compressible Multi-scale Flows

David Iampietro (1, 2) , Frédéric Daude (2) , Pascal Galon (3) , Jean-Marc Hérard (1, 2)

1 AMU - Aix Marseille Université
2 EDF - EDF
3 CEA - Commissariat à l'énergie atomique et aux énergies alternatives

The method presented below focuses on the numerical approximation of the Euler compressible system. It pursues a twofold objective: being able to accurately follow slow material waves as well as strong shock waves in the context of low Mach number flows. The resulting implicit-explicit fractional step approach leans on a dynamic splitting designed to react to the time fluctuations of the maximal flow Mach number. Would the latter rise suddenly, the IMEX scheme, so far driven by a material-wave Courant number, would turn into a time-explicit approximate Riemann solver constrained by an acoustic-wave Courant number. One dimensional low Mach number test cases involving single or multiple waves confirm that the present approach is as accurate and efficient as an IMEX Lagrange-Projection method. Besides, a pragmatic stability study suggests that the resulting IMEX scheme is stable, whatever the Mach number, for a material-wave Courant number of order unity.

Mots clés: Fractional Step; Implicit-Explicit Schemes; Multi-scale Flows; Low Mach Number; Relaxation Schemes; Hyperbolic

Domaines: Physique mathématique [math-ph]; Analyse numérique [math.NA]

David Iampietro, Frédéric Daude, Pascal Galon, Jean-Marc Hérard. A Mach-Sensitive Implicit-Explicit Scheme Adapted to Compressible Multi-scale Flows. 2017. ⟨hal-01531306v1⟩