Approaching the efficiency of stationary-body methods in a strongly coupled immersed boundary framework for fluid-structure interaction

Strongly coupled immersed boundary (IB) methods strictly enforce the no-slip constraint on the body by solving the nonlinear fluid and structural equations of motion simultaneously. Handling this constraint requires solving several large dimensional systems that scale by the number of grid points in the flow domain even though the nonlinear constraints only scale by the small number of points used to represent the fluid-structure interface. In this talk, we will address the computational bottleneck of such strongly coupled IB methods wherein several costly large dimensional systems are solved for a small number of body variables. Our proposed approach is motivated by the efficient strategy employed in stationary-body IB methods---we precompute a matrix that encapsulates the large dimensional system so that the prohibitive large scale operations need not be performed at every time step. This precomputation process yields a small-dimensional system for the constraint equations which can solved at minimal computational cost while time advancing the equations. We also present a parallel implementation that scales favorably across multiple processors. The accuracy, computational efficiency and scalability of our approach are demonstrated on several two dimensional flow problems.