Immersed Boundary Projection Method for Boundaries With Slip Velocities

ABSTRACT

We present a formulation of the immersed boundary method for incompressible flows over bodies with surface slip described by the Navier boundary condition. In the present method, the wall slip velocity and the boundary force are implicitly determined through a projection that enforces both the boundary conditions and the divergence‐free constraint of the velocity field. The present method is first‐order accurate in space and fourth‐order accurate in time, providing a consistent way to evaluate the velocity gradient on the boundary, which is challenging in conventional continuous forcing approaches. The validation results from the simulation of the flow past two‐dimensional stationary and moving bodies are in good agreement with previous experimental and numerical results for a wide range of slip lengths on the surface, including the no‐slip case. The spatial resolution required to reproduce the body‐fitted mesh solution is numerically evaluated for Reynolds numbers below 100, where the wall slip velocity plays an important role.