G. Comini et al., A STREAMFUNCTION-VORTICITY-BASED FINITE-ELEMENT FORMULATION FOR LAMINAR-CONVECTION PROBLEMS, Numerical heat transfer. Part B, Fundamentals, 28(1), 1995, pp. 1-22
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.