Thermodynamically consistent phase-field modeling and numerical simulation for two-phase fluid-solid dynamics

TL;DR

This paper develops a thermodynamically consistent phase-field model for two-phase fluid-solid systems, introduces a numerical scheme that preserves energy dissipation, and demonstrates its effectiveness through simulations including reacting flows.

Contribution

It presents a new coupled Cahn-Hilliard Navier-Stokes model with a fully-discrete energy-stable numerical method for two-phase fluid-solid dynamics.

Findings

Numerical experiments confirm energy dissipation properties.

Method successfully models complex geometries and reacting flows.

Comparative study of solution strategies enhances computational approaches.

Abstract

We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete numerical method that relies on a continuous finite element approach and a semi-implicit time-stepping method. As the main theoretical result we show that the fully-discrete method satisfies a discrete analog of the free energy dissipation inequality. Numerical experiments confirm the theoretical findings and show the applicability of the method for realistic settings including an extension to chemically reacting flow. In this context, we provide a preprocessing strategy that enables computing fluid flow in complex geometries given a sharp-interface formulation of the initial phase distribution. Moreover, we briefly introduce different solution strategies for the novel discretization based on the monolithic and partitioned solution paradigms and assess these in a comparative study.