Fluid–structure interaction for a pressure driven flow

In this article we discuss the application of a Lagrange multiplier based fictitious domain method for the simulation of the motion of two rigid flaps in an unsteady flow generated by pressure gradients. The distributed Lagrange multiplier technique can be an important numerical tool to design a mechanical heart valve and investigate the flow around rigid flaps without assuming the motion of the flaps in advance. Here, we derive a mathematical formulation of a fluid–structure interaction model that includes the generalized Neumann boundary conditions on the upstream and downstream boundaries along with rigid flaps rotating around the fixed points. The solution method includes the finite element approximation for space and the Marchuk–Yanenko operator splitting scheme for time discretization. This study presents the numerical results obtained for flap motion for a simple sinusoidal wave. Furthermore, these simulations are extended to apply to a more complex biological system involving the systolic phase of the pulse pressure.