Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

TL;DR

This paper develops a thermodynamically consistent mathematical model and entropy stable numerical scheme for simulating non-isothermal, multi-component two-phase flows with realistic equations of state, capturing complex fluid interactions.

Contribution

It introduces a rigorous model based on thermodynamics and Onsager's principle, and proposes an entropy stable numerical method that preserves energy laws in simulations.

Findings

The model characterizes compressibility and partial miscibility of fluids.

The numerical scheme is proven to be unconditionally entropy stable.

Numerical results validate the accuracy and stability of the proposed method.

Abstract

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager's reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.