An Immersed Boundary Projection Method for Dynamics of Rigid Bodies Interacting with Fluid Flows

The fast immersed boundary projection method using a nullspace approach and multi-domain far-field boundary conditions developed by Colonius and Taira (Comput. Methods Appl. Engrg., 2008) is further extended to simulate dynamics of rigid bodies interacting with fluid flows. Dynamics of rigid bodies is characterized by the velocity of the center of mass and the angular velocity about the center of mass, which are governed by the translational and rotational equations of motion involving boundary forces. By introducing the summation and distribution operators, equations of motion are coupled with the incompressible Navier-Stokes equations through the no-slip constraint and boundary forces. Boundary forces are regarded as Lagrange multipliers that enable the no-slip constraint to be implicitly determined to arbitrary precision without associated time-step restrictions. Through projections, the current method removes not only slip component of the velocity field but also components of rigid-body dynamics that do not satisfy equations of motion. Results from simulating an impulsively-rotated circular shell in a quiescent fluid are in good agreement with numerical solutions of the analytical model.