Phase-field formulation of a fictitious domain method for particulate flows interacting with complex and evolving geometries

A distributed Lagrange multiplier/fictitious domain method in a phase-field formulation for the simulation of rigid bodies in incompressible fluid flow is presented. The phase-field method yields an implicit representation of geometries and thus rigid body particulate flows within arbitrary geometries can be simulated based on a fixed Cartesian grid. Therefore, a phase-field based collision model is introduced in order to address contact of particles with arbitrary solid structures as boundaries. In addition, grain growth within the boundary geometry can be considered leading to changes in its shape during the simulation. The method is validated on benchmark problems and a convergence study is performed. Multiple numerical experiments are carried out in order to show the methods' capability to simulate problems with differently shaped rigid bodies and particulate flows involving complex boundary geometries like foam structures.