An immersed boundary method on Cartesian mesh with local refinement appliced to heat convection problems

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.

The incompressible Navier-Stokes equations with heat transfer are solved by an implicit pressure correction method on Cartesian mesh with local refinement. A simple immersed boundary method is developed to treat arbitrary solid bodies in the flow field. A direct forcing term was added to cells inside the immersed body to enforce the Dirichlet boundary condition for velocity and temperature. This 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 forcing term 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 tests are computed to verify this simple immersed boundary method, including the steady and unsteady forced convection over a circular cylinder and the natural convection over a heated circular cylinder inside a square cavity.