Random sampling remap for compressible two-phase flows

Abstract

International audienceIn this paper, we address the problem of solving accurately gas-liquid compressible flows, without pressure oscillations at the gas-liquid interface. We introduce a new Lagrange-projection scheme based on a random sampling technique of Chalons and Goatin. We compare it to a Ghost Fluid approach introduced previously. Despite the non-conservative feature of the schemes, we observe the numerical convergence towards the relevant weak solution, for shock-contact interaction test cases. Finally, we apply the new scheme to the computation of the oscillations of a spherical air bubble inside water

Two-fluid compressible simulations on GPU cluster

“…The method was first proposed in [6] for a particular traffic flow model. It does not introduce a mixture zone and extends the one-dimensional method described in [2]. More precisely, we construct a numerical scheme that preserves the hyperbolic domain without diffusion H,…”

Modeling binary alloy solidification by a random projection method

“…Finally Colella had improved the method of Chorin in [30,31], especially by introducing the so-called van der Corput pseudo-random sequence. The technique has been widely used for hyperbolic problems which exhibit sharp discontinuities: in [32] for nonconservative hyperbolic problems for compressible materials, in [33,34] for traffic flow models, in [35] for compressible fluid-particule interaction or in [36,37] for the simulation of two-fluid flows.…”

A coupled well-balanced and random sampling scheme for computing bubble oscillations

“…initial data for which the quantities ϕ, s, Q, H are constant); • for a flow in a duct with constant cross-section ducts, it computes exactly the contact discontinuities, with no smearing at the interface; • if at the initial time the mass fraction is in {0, 1}, then this property is exactly preserved at any time. For detailed proofs, we refer to [1,6]. Some other subtleties are given in the same references.…”

“…We construct a sequence of pseudo-random numbers ω n ∈ [0, 1[. In practice, we consider the (5, 3) van der Corput sequence [1]. According to this number we take…”

“…• For two-fluid flows the pressure oscillations phenomenon (see [2,8] for instance) can be cured by a recent tool developed in [1,4]. It is based on an ALE (Arbitrary Lagrangian Eulerian) scheme followed by a random sampling projection step.…”