Radial basis function collocation method solution of natural convection in porous media
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 1 March 2004
Abstract
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.
Keywords
Citation
Šarler, B., Perko, J. and Chen, C. (2004), "Radial basis function collocation method solution of natural convection in porous media", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 14 No. 2, pp. 187-212. https://doi.org/10.1108/09615530410513809
Publisher
:Emerald Group Publishing Limited
Copyright © 2004, Emerald Group Publishing Limited