OPEN BOUNDARY-CONDITIONS FOR THE STREAMFUNCTION-VORTICITY FORMULATIONOF UNSTEADY LAMINAR CONVECTION

The streamfunction-vorticity formulation is used to analyze unsteady l aminar-convection problems in two dimensional incompressible flows. Th e Bubnov-Galerkin finite-element method and a sequential procedure are employed to discretize and solve the governing differential equations . Very accurate results are obtained by employing ''advective derivati ve conditions'' at the outflow for all the variables involved. The bou ndary conditions for the streamfunction at internal walls are imposed during the assembly process, and the vorticity at inflow and wall boun daries is evaluated in the framework of the streamfunction equation. T he accuracy of the approach is demonstrated by the solution of two wel l-known benchmark problems concerning forced convection over a circula r cylinder in crossflow and mired convection in a plane channel heated from below.