Immersed Boundary Projection Method for Navier Slip Boundaries

Abstract: A formulation of the immersed boundary method for incompressible flow over bodies with surface slip described by the Navier boundary condition is presented. In the present method, the wall slip velocity and the boundary force are determined implicitly through a projection to satisfy the boundary conditions and the divergence-free condition of the velocity field as constraints. The present method is first-order accurate in space and fourth-order accurate in time, overcoming the difficulty of the conventional continuous forcing approaches to accurately evaluate the velocity gradient on the boundary. Results from the simulation of the flow past stationary and moving circular cylinders are in good agreement with previous experimental and numerical results for a wide range of slip length on the surface, including the no-slip case.