A second-order time accurate semi-implicit method for fluid–structure interaction problems

Abstract

This paper is concerned with numerical solution of fluid–structure interaction (FSI) problems involving an incompressible viscous flow and an elastic structure. A semi-implicit partitioned method with second-order temporal accuracy is proposed. The method separates the pressure term of the fluid equations and strongly couples it to the structure, while the remaining fluid terms and the geometrical nonlinearities are treated explicitly. A second-order projection method is used to solve the fluid equations and also as a framework for the FSI coupling. Particular attention is paid to the boundary conditions for fluid equations and the accuracy of the fluid pressure on the common interface. The proposed coupling method retains the second-order accuracy for fully-coupled nonlinear FSI problems. Extensive numerical tests are carried out on a number of benchmark FSI problems and the second-order temporal accuracy for all the variables of interest (fluid velocity and pressure, and structural displacement) is demonstrated.