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

We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the reactive 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. Our main theoretical result establishes that the fully discrete method satisfies an analog of the free energy dissipation inequality, provided that the phase-field variable remains within prescribed bounds. Numerical experiments confirm the theoretical findings and show the applicability of the method for realistic settings. 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.