A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion

We present a computational algorithm for fully resolved numerical simulation (FRS) of rigid and deforming bodies moving in fluids. Given the deformation of the body in its own reference frame, the method solves for the swimming velocity of the body together with the surrounding flow field, and the hydrodynamic forces on the body. We provide the mathematical foundation of the algorithm based on distributed Lagrange multipliers, and show that it naturally connects with vortex methods through a vorticity source at the interface. We demonstrate applications to rigid and flexible bodies, membranes, and bodies with a propelling membrane attached to them. In contrast to some existing methods, the swimming velocity of the body is not prescribed but is computed along with the forces, without requiring a body-fitted grid. The algorithm is designed to be fast, efficient, and easy to implement in existing fluid dynamics codes for practical solid–fluid problems in engineering and biology.