An Anti-Diffusive Numerical Scheme for the Simulation of Interfaces between Compressible Fluids by Means of a Five-Equation Model

F Lagoutière (1) , Samuel Kokh

1 LJLL - Laboratoire Jacques-Louis Lions

We propose a discretization method of the five-equation model with isobaric closure presented in [2, 3] for the simulation of compressible two-phase flows with interfaces. This numerical solver is a Lagrange-Remap scheme that aims at controlling the numerical diffusion of the interface between both fluids thanks to the seminal ideas of [13, 6, 7]. This method does not involve any interface reconstruction procedure. The solver is equipped with built-in stability and consistency properties and is conservative with respect to mass, momentum, total energy and partial mass. This numerical scheme works with a very broad range of equations of state, including tabulated laws. Properties that ensure a good treatment of the Riemann invariants across the interface are demonstrated. As a consequence, the numerical method does not create spurious pressure oscillations at the interface. We show one-dimensional and two-dimensional classical numerical tests and comparisons with the classical upwind Lagrange-Remap approach.

Mots clés: two-phase flows; interface problems; anti-diffusive scheme Contents

Domaines: Analyse numérique [math.NA]

F Lagoutière, Samuel Kokh. An Anti-Diffusive Numerical Scheme for the Simulation of Interfaces between Compressible Fluids by Means of a Five-Equation Model. Journal of Computational Physics, inPress. ⟨hal-03827923⟩