A penalty immersed boundary method for a rigid body in fluid

We extend the penalty immersed boundary (pIB) method to the interaction between a rigid body and a surrounding fluid. The pIB method is based on the idea of splitting an immersed boundary, which here is a rigid body, notionally into two Lagrangian components: one is a massive component carrying all mass of the rigid body and the other is massless. These two components are connected by a system of stiff springs with 0 rest length. The massless component interacts with the surrounding fluid: it moves at the local fluid velocity and exerts force locally on the fluid. The massive component has no direct interaction with the surrounding fluid and behaves as though in a vacuum, following the dynamics of a rigid body, in which the acting forces and torques are generated from the system of stiff springs that connects the two Lagrangian components. We verify the pIB method by computing the drag coefficients of a cylinder and ball descending though a fluid under the influence of gravity and also by studying the interaction of two such descending cylinders and likewise the interaction of two such descending balls. The computational results are quite comparable to those in the literature. As a further example of an application, we include a freely falling maple seed with autorotation.