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

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 N 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. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).