The immersed interface method for 3D rigid objects in a flow

In the immersed interface method, an object moving in a fluid is treated as the fluid enclosed by a singular force, and the singular force enters numerical schemes through jump conditions. In this talk, I will present a boundary condition capturing approach to determine the singular force for a 3D moving rigid object. Unlike many \emph{ad hoc} penalty approaches, this approach is explicit but numerically stable. I will demonstrate its accuracy, stability and efficiency using flow due to an oscillating sphere/torus and flow due to a flapping wing.