An Eulerian method for mixed soft and rigid body interactions in fluids

Fluid-solid interaction problems are encountered in many engineering and biological applications, but are challenging to simulate due to the coupling between the two material phases. Here, we use the reference map technique, a fully Eulerian approach for fluid-solid interaction that is simple to implement and capable of simulating complex multi-body interactions of soft solids. We extend the technique to simulate rigid solids in an incompressible fluid, using a projection step formulated as a composite linear system that simultaneously enforces the rigidity and incompressibility constraints. This projection step is solved efficiently using a Schur complement and a multigrid preconditioner. Several examples including a single body, multiple rigid bodies, and soft-rigid combinations will be presented.