Simulations of Complex Flows and Fluid-Structure Interaction Problems on Fixed Cartesian Grids

A finite-difference based approach for computing flows with complex moving solid three-dimensional boundaries on fixed Cartesian grid has been developed. Internal solid boundaries are represented by “blocking off” the grid cells inside the boundary. This results in considerably increased computing efficiency over conventional body-conformal structured grid methods. A mixed explicit-implicit fractional step method is employed for time integration while the spatial discretization scheme is based on a second-order accurate central-difference scheme. The pressure Poisson equation is solved using algebraic multigrid as well as Krylov subspace based methods. The current simulation methodology is validated by simulating various canonical flows. Further, we compute the flow generated by a moving body as well as the flow generated by a synthetic jet in order to demonstrate the capabilities of this solver.