Computation of incompressible flows with immersed bodies by a simple ghost cell method

The incompressible Navier-Stokes equations are solved by an implicit pressure correction method on Cartesian meshes with local refinement. A simple and stable ghost cell method is developed to treat the boundary condition for the immersed bodies in the flow field. Multigrid methods are developed for both velocity and pressure correction to enhance the stability and convergence of the solution process. It is shown that the spatial accuracy of the method is second order in L₂ norm for both velocity and pressure. Various steady and unsteady flows over a 2D circular cylinder and a 3D sphere are computed to validate the present method. The capability of the present method to treat a moving body is also demonstrated.