Benchmark Boundary Element Solutions for Some Problems Governed by the Boussinesq Equations

The boundary element formulation developed previously by the authors for incompressible isothermal viscous fluid flows is extended for non-isothermal flows governed by Boussinesq equations. The new boundary element method is applied to the classical Rayleigh-Benard problem and to a stratified flow over a backward-facing step. In all cases, the boundary element results are in good agreement with published finite element solutions. However, in some instances, the boundary element solutions are more accurate, particularly in terms of resolving surface tractions and heat fluxes.