A SIMPLE MOMENTUM FORCING METHOD ON UNSTRUCTURED CARTESIAN MESH FOR IMMERSED BODIES IN INCOMPRESSIBLE FLOWS

Abstract. The incompressible Navier-Stokes equations are solved by an implicit pressure correction method on unstructured Cartesian meshes. A simple immersed boundary method is developed to treat arbitrary solid bodies in the flow field. A direct momentum forcing term was added to cells inside the immersed body to enforce the no-slip boundary condition. This momentum forcing is also assumed to have an active range of one cell size normal to the immersed boundary, acting on fluid cells external to the immersed body. For those cells within the active range, the amount of momentum forcing added to the cell is scaled by the normal distance from the cell center to the body surface. The same pressure Poisson equation is applied to the entire flow field without distinguishing whether it is inside or outside the immersed body. Various steady and unsteady flows over a circular cylinder are computed to verify the present method. The flow of an ellipse in Figure-8 motion is also computed to demonstrate the capability of the present method to treat moving bodies. Dartzi Pan and Tzung-Tza Shen