New SFB 1313 publication, published in the scientific journal Computer Methods in Applied Mechanics and Engineering. The work has been developed in the context of the SFB 1313 research project C02.
Authors
- Cedric Riethmüller (University of Stuttgart)
- Lars von Wolff (SFB 1313 Alumnus)
- Dominik Göddeke (University of Stuttgart, former SFB 1313 researcher)
- Christian Rohde
Abstract
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.