A semi-implicit finite element formulation of the partitioned method for fluid-structure interaction based on a flux boundary condition of pressure equation

A semi-implicit algorithm of the partitioned method is newly proposed for fluid-structure interaction using the finite element method. In particular, an incompressible fluid flow is solved by a splitting method, and the solid domain of a reference configuration is solved by a total Lagrangian approach. While the viscous traction of the fluid flow is explicitly estimated in a coupling algorithm, the pressure traction from the fluid flow is implicitly coupled with the solid motion through iterative computations separately performed on the fluid and then the solid domain. By employing a weak formulation of the pressure Poisson equation based on a flux (fluid velocity) boundary condition, solid motion is successfully coupled with the pressure equation during the iterative computation. The proposed method has been found to be more efficient compared with not only a fully-implicit scheme of the partitioned method, but also a monolithic formulation in terms of CPU time and memory usage. Lastly, the parallel implementation of the proposed method is very attractive due to the fluid-solid coupling through a simple pressure Poisson equation.