An Eulerian method for mixed soft and rigid body interactions in incompressible 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 propose a fully Eulerian approach for solving fluid-solid interactions that is simple to implement and capable of simulating complex multi-body interactions. When the solid is rigid, a projection step is formulated as a composite linear system that simultaneously enforces the rigidity and incompressibility constraints. When the solid is soft, a reference map technique is applied to characterize the body deformation in an Eulerian framework. Several examples including a single body, multiple bodies, and soft-rigid combinations will be presented, with potential applications to biological systems.