On the Immersed Boundary Method with Time-Filter-SAV for Solving Fluid–Structure Interaction Problem

In this work, the immersed boundary method with time filter and scalar auxiliary variable techniques is studied to solve the fluid–structure interaction problems. For the fluid flow, we first use the backward Euler differentiation formula in temporal discretization, we then employ the time filter technique to improve its convergence order, the scalar auxiliary variable strategy is visited to decouple the fluid equations and achieve fast solutions. We adopt the immersed boundary method to build the connection between the fluid and the structure, as well as characterize the deformations of the structure. We approximate the fluid–structure interaction model by the finite element method in space. The semi-discrete and fully-discrete implicit numerical schemes are proposed followed with unconditionally stability properties. We carry out several numerical experiments to validate the convergence behaviors and efficiency of the algorithms.