A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method

We address the numerical simulation of fluid-structure interaction problems dealing with an incompressible fluid whose density is close to the structure density. We propose a semi-implicit coupling scheme based on an algebraic fractional-step method. The basic idea of a semi-implicit scheme consists in coupling implicitly the added-mass effect, while the other terms (dissipation, convection and geometrical non-linearities) are treated explicitly. Thanks to this kind of explicit-implicit splitting, computational costs can be reduced (in comparison to fully implicit coupling algorithms) and the scheme remains stable for a wide range of discretization parameters. In this paper we propose to derive this kind of splitting from the algebraic formulation of the coupled fluid-structure problem (after finite-element space discretization). This approach extends for the first time to fluid-structure problems the algebraic fractional step methodology that was previously advocated to treat the pure fluid problem in a fixed domain. More particularly, for the specific semi-implicit method presented in this report we adapt the Yosida scheme to the case of a coupled fluid-structure problem.