A Simple Method for Compressible Multifluid Flows

Abstract

Abstract. A simple second order accurate and fully Eulerian numerical method is presented for the simulation of multifluid compressible flows, governed by the stiffened gas equation of state, in hydrodynamic regime. Our numerical method relies on a second order Godunov-type scheme, with approximate Riemann solver for the resolution of conservation equations, and a set of nonconservative equations. It is valid for all mesh points and allows the resolution of interfaces. This method works for an arbitrary number of interfaces, for breakup and coalescence. It allows very high density ratios (up to 1000). It is able to compute very strong shock waves (pressure ratio up to 10 5 ). Contrary to all existing schemes (which consider the interface as a discontinuity) the method considers the interface as a numerical diffusion zone as contact discontinuities are computed in compressible single phase flows, but the variables describing the mixture zone are computed consistently with the density, momentum and energy. Several test problems are presented in one, two, and three dimensions. This method allows, for example, the computation of the interaction of a shock wave propagating in a liquid with a gas cylinder, as well as Richtmeyer-Meshkov instabilities, or hypervelocity impact, with realistic initial conditions. We illustrate our method with the Rusanov flux. However, the same principle can be applied to a more general class of schemes.

Finite volume simulation of cavitating flows

“…According to our first experiments, numerical pressure oscillations appear at the interface between air and water [3]. These oscillations are similar to those observed in many works about two-phase flows [1], [19], [27], [31]... It must be pointed out that in the present work we observed no pressure oscillations at the interface between liquid and vapor for we have allowed mass transfers between these two phases.…”

Two-fluid compressible simulations on GPU cluster

“…This artificial mixing zone implies a loss of velocity and pressure equilibrium at the interface. It is possible to recover a better equilibrium by relaxing the conservation property of the scheme as in [17].…”

Applications of the finite volumes method for complex flows: From the theory to the practice

“…On the discrete side, these forms are not equivalent, and the one that is presented in (40), (45) plays a special role. We used the trick of Abgrall and Saurel described in [17] and [2] in order to get a numerical scheme that preserves the constant velocity and pressure states. It is then possible to compute the wave evolution.…”

“…It can be generalized, with some adaptations, to (17) and (18). Let τ be a time step and h a space step.…”

“…It has been used by several authors for multi-fluid flows computations [17], [2], etc. The sound speed for this EOS is given by…”