Pressure relaxation procedures for multiphase compressible flows

Abstract

This paper deals with pressure relaxation procedures for multiphase compressible flow models. Such models have nice mathematical properties (hyperbolicity) and are able to solve a wide range of applications: interface problems, detonation physics, shock waves in mixtures, cavitating flows, etc. The numerical solution of such models involves several ingredients. One of those ingredients is the instantaneous pressure relaxation process and is of particular importance. In this article, we present and compare existing and new pressure relaxation procedures in terms of both accuracy and computational efficiency. Among these procedures we enhance an exact one in the particular case of fluids governed by the stiffened gas equation of state, and approximate procedures for general equations of state, which are particularly well suited for problems with large pressure variations. We also present some generalizations of these procedures in the context of multiphase flows with an arbitrary number of fluids. Some tests are provided to illustrate these comparisons. Copyright © 2005 John Wiley & Sons, Ltd.

A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows

“…When dealing with more sophisticated formulations, as for example the 7-equation model, extra ingredients have to be presented, such as velocity, pressure and temperature relaxation solvers, as done for example in [9,10]. Here, there is a single step Here Y l,g , α l,g , ρ l,g denote respectively the mass fraction, the volume fraction and the material density of the liquid (l subscript) and gas (g subscript) phases.…”

“…This last model is a 7-equation formulation assuming mechanical, thermal and chemical disequilibrium. Thereby, finding local thermodynamic equilibrium requires extra ingredients such as velocity, pressure and temperature relaxation solvers such as the ones given in [9,10].…”

Simulation of Multiphase Flows with Strong Shocks and Density Variations

“…The classical MUSCL scheme has been used to obtain the second order accuracy in both space and time as described in [4]. Whereas, the pressure relaxation operator has been solved using the iterative method that is described in [5]. The second test is numerically challenging shock bubble interaction test.…”

A Cell-Centered Multiphase ALE Scheme With Structural Coupling

“…A number of pressure-equilibrium models are discussed in the literature (e.g. [57,67]). The current technique is based on the method of Tipton [68].…”