A penalty-projection algorithm for a monolithic fluid-structure interaction solver

In this paper we propose a new iterative penalty-projection algorithm for a monolithic fluid-structure interaction solver. Projection methods, that split the computation of the velocity from the pressure, are very popular in fluid dynamics since the boundary errors generated by the projection method are localized mainly near the boundary layers where the incorrect pressure boundary conditions are imposed. However, when solid regions are taken into account, the pressure projected field cannot satisfy fully coupled boundary constraints imposed on external solid surfaces such as stress-free conditions, and, due to the rigidity of the medium, the boundary errors propagate deeply in the interior. In order to reduce the projection errors we propose a one-step penalty-projection method in the fluid domain and an iterative penalty-projection method in the solid region. This technique decouples the pressure-velocity degrees of freedom and, as a consequence, the computational cost. In order to verify the accuracy and robustness of the proposed method we compare the results between this splitting velocity-pressure algorithm and the coupled one. These numerical results show stability and robustness of the proposed algorithm with a strong reduction of the computational effort.