A new method to discretize a model for isothermal flow with a multi-component equation of state

Abstract

In this paper we will discuss numerical problems in a phase function model with a multi-component equation of state. It is a sub-model of a diffuse interface model, using a phase field equation, that was introduced by Dreyer et al. in 2014. This model was proposed to describe chemically reacting fluid mixtures consisting of constituents where phase transitions between a liquid and a vapor phase may occur. The phase field indicates the present phase or the transition layer. The discretization of the model with shock capturing methods for the hyperbolic sub-part is a challenge. One difficulty is that the equation of state has a steep gradient in the density. Moreover, numerical viscosity in diffusive interface computations leads to intermediate values that are unphysical. Our sub-model contains these problems in a nutshell. We develop a solution strategy and apply the new method to several test cases.