A partitioned framework for coupling LBM and FEM through an implicit IBM allowing non-conforming time-steps: Application to fluid-structure interaction in biomechanics

Abstract

This paper presents a partitioned framework for the numerical simulation of fluid-structure interactions by coupling the lattice Boltzmann method (LBM) and the finite element method (FEM). The two numerical methods LBM and FEM are coupled with an implicit immersed boundary method (IBM) in a strong way, which ensures exactly the no-slip condition and the continuities of velocity and stress at the fluid-solid interface and each instant in time. In the proposed partitioned coupling procedure, the coupling system of equations are first established and then condensed to the interface. By solving the condensed coupling system of equations, the interface force field is obtained and sent to both solvers to accomplish time integrations in each sub-domain. In addition, two strategies based on linear interpolation in time are proposed to handle the cases with non-conforming time-steps in the fluid and solid sub-domains. Through several 2D and 3D numerical test-cases on the mechanical heart valve, the fluid-induced vibration of a deformable solid beam, the flapping flag, the proposed coupling framework is validated with good agreements with references. Finally, a test-case on the interaction between the blood flow and the aortic valve is carried out, showing the applicability of the present framework in realistic biomechanical applications.