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Radial basis function collocation method solution of natural convection in porous media. (English) Zbl 1103.76361
Summary: This paper describes the solution of a steady-state natural convection problem in porous media by the radial basis function collocation method (RBFCM). This mesh-free (polygon-free) numerical method is for a coupled set of mass, momentum, and energy equations in two dimensions structured by the Hardy’s multiquadrics with different shape parameter and different order of polynomial augmentation. The solution is formulated in primitive variables and involves iterative treatment of coupled pressure, velocity, pressure correction, velocity correction, and energy equations. Numerical examples include convergence studies with different collocation point density and arrangements for a two-dimensional differentially heated rectangular cavity problem at filtration Rayleigh numbers $$Ra^*=25$$, 50 and 100, 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 in terms of mid-plane velocity components, mid-plane and insulated surface temperatures, streamfunction minimum, and Nusselt number.

MSC:
 76M30 Variational methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 76E06 Convection in hydrodynamic stability
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