On pressure boundary conditions for thermoconvective problems

Abstract

Solving numerically hydrodynamical problems of incompressible fluids raises the question of handling first order derivatives (those of pressure) in a closed container and determining its boundary conditions. We research several pressure boundary conditions for the primitive variables formulation of thermoconvective problems. In particular we study the Marangoni instability of an infinite fluid layer and we show that the numerical results with a Chebyshev collocation method are highly correspondent to the exact ones. These ideas have been applied to linear stability analysis of the B\'enard-Marangoni (BM) problem in cylindrical geometry and the results obtained have been very accurate.