BOUNDARY-CONDITIONS FOR FINITE-ELEMENT SIMULATIONS OF CONVECTIVE FLOWS WITH ARTIFICIAL BOUNDARIES

We examine the use of natural boundary conditions and conditions of th e Sommerfeld type for finite element simulations of convective transpo rt in viscous incompressible flows. We show that natural boundary cond itions are superior in the sense that they always provide a correct bo undary condition, as opposed to the Sommerfeld-type conditions, which can lead to a singular formulation and a great loss of accuracy. For t he Navier-Stokes equations, the natural boundary conditions must be co mbined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.