Penalty-projection Method for a Monolithic Fluid Structure Interaction Solver

Abstract. In this paper we present the results of Fluid-Structure Interaction (FSI) computations of an incompressible solid object and laminar incompressible viscous flows using a combined penalty-projection algorithm. The system consists of a fluid region governed by Navier-Stokes equations and a solid domain described by elastic and hyperelastic structure mechanical equations. In particular we impose the incompressibility constraint both in the solid hyperelastic and incompressible fluid region by using an iterative projection method which decouples pressure and velocity field. This technique reduces the degrees of freedom of the problem decreasing the computational cost of the solution algorithm. However in the projection pressure equation is not possible to impose the physical boundary conditions and consistent errors are generated on the solid boundary. In order to correct this boundary error due to the decoupling projection algorithm a combined projection-penalty method is introduced. The fluid and the solid incompressibility constraint are imposed in a monolithic approach over all the fluid and solid unknowns when large displacement occurs. In order to verify the accuracy of the proposed method we compare the results of the projection with the projection-penalty and coupled algorithm. These analyzed cases show stability and robustness of the proposed algorithm for appropriate value of the penalty parameter together with a reduction of the computational effort compared with that needed by the coupled algorithm.