A robust implicit-explicit acoustic-transport splitting scheme for two-phase flows

Simon Peluchon (1) , Gérard Gallice (1) , Luc Mieussens (2, 3)

1 CESTA - Centre d'études scientifiques et techniques d'Aquitaine
2 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
3 IMB - Institut de Mathématiques de Bordeaux

In this paper, a splitting strategy to simulate compressible two-phase flows using the five-equation model is presented. The main idea of the splitting is to separate the acoustic and transport phenomena. The acoustic step is solved in a non-conservative form using a scheme based on an approximate Riemann solver. Since the acoustic time step induced by the fast sound velocity is very restrictive, an implicit treatment of this step is performed. For the transport step driven by the slow material waves, an explicit scheme is used. Although non-conservative forms are used to derive numerical schemes for the two steps, the overall scheme resulting from this splitting operator strategy is conservative. It preserves contact discontinuities and reveals to be very robust compared to a standard unsplit scheme. Numerical simulations of compressible two-phase flows are presented on two-dimensional structured grids. The implicit-explicit strategy allows large time steps, which do not depend on the fast acoustic waves.

Mots clés: two-phase flows; positive Riemann solver; implicit scheme

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Simon Peluchon, Gérard Gallice, Luc Mieussens. A robust implicit-explicit acoustic-transport splitting scheme for two-phase flows. Journal of Computational Physics, 2017, ⟨10.1016/j.jcp.2017.03.019⟩. ⟨hal-01448468⟩