A Review of Interface-Driven Adaptivity for Phase-Field Modeling of Fluid-Structure Interaction

In this paper, we systematically review interface-driven mesh adaptation procedures for the phase-field modeling of fluid-structure interaction problems. One of the popular ways of handling fluid-structure interaction problems involving large solid deformations is the fully Eulerian approach. In this procedure, we use a fixed computational grid over which a diffused interface description can be used to evolve the fluid-structure boundary. The Eulerian solid representation and a diffuse interface method necessitate the use of adaptive mesh refinement to achieve reasonable accuracy for the problem at hand. We explore the usage of mesh refinement techniques for such FSI problems and focus specifically on interface-driven adaptivity. We present comparisons among various error indicators for the adaptive procedure of the unstructured mesh. We finally explore some possible future directions and challenges in the field.