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.