A STREAMFUNCTION-VORTICITY-BASED FINITE-ELEMENT FORMULATION FOR LAMINAR-CONVECTION PROBLEMS

The finite-element method is used to solve mixed-, forced-, and natura l-convection problems in two-dimensional incompressible laminar flows. The streamfunction-vorticity equations are uncoupled and solved in se quence with the energy equation. The wall vorticity is evaluated in th e framework of the streamfunction equation, and particular care is tak en to specify inflow and outflow boundary conditions properly. The res ulting scheme achieves convergence without the traditional need for up winding, even for very high values of the Reynolds and the Rayleigh nu mbers. Stability and accuracy of the approach are demonstrated by the solution of three well-known test problems concerning mixed and forced convection downstream of a backward-facing step, and natural convecti on in a heated square cavity.