Natural convection in porous media – dual reciprocity boundary element method solution of the Darcy model. (English) Zbl 0972.76071
Summary: This paper describes the solution of a steady-state 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 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 and linear boundary field discretizations for differentially heated rectangular cavity problems at filtration with Rayleigh numbers of \(Ra^*= 25\), 50, and 100 and aspect ratios of \(A=1/2\), 1, and 2. The solution is assessed by comparison with reference results of the fine mesh finite volume method.
MSC:
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
| 76R10 | Free convection |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
primitive variables; steady-state natural convection; porous media; dual reciprocity boundary element method; fundamental solution; Laplace equation; thin plate splines; convergence; heated rectangular cavity; filtrationReferences:
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