Dual reciprocity boundary element method solution of natural convection in Darcy–Brinkman porous media

Abstract

This paper describes the solution of a steady natural convection problem in porous media by the dual reciprocity boundary element method. The boundary element method for the coupled set of mass, momentum, and energy equations in two-dimensions is structured by the fundamental solution of the Laplace equation. The dual reciprocity method is based on augmented scaled thin plate splines. Numerical examples include convergence studies with different mesh size, uniform and non-uniform mesh arrangement, and constant, linear, and quadratic boundary field discretisations for differentially heated rectangular cavity problems at filtration with Rayleigh number of Ra ∗=25, 50, and 100, Darcy numbers Da=10 −3, and 10 −5, and aspect ratios A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine-mesh finite volume method.