An accurate solution procedure for fluid flow with natural convection

Abstract

We consider the Boussinesq model of buoyancy driven fluid flows. This nonlinear system is solved numerically using a two level finite element method. On the first level, a nonlinear system is solved on a very coarse mesh. Thereafter, a linear system is solved on a fine mesh. In a standard approach, one might obtain the numerical solution from a discretization of the original, nonlinear system using the same fine mesh. Both solutions are of equal order of accuracy if the mesh widths are properly balanced. Therefore the two level method is very efficient.