G. Comini et al., OPEN BOUNDARY-CONDITIONS FOR THE STREAMFUNCTION-VORTICITY FORMULATIONOF UNSTEADY LAMINAR CONVECTION, Numerical heat transfer. Part B, Fundamentals, 31(2), 1997, pp. 217-234
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.