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ARTICLE

Numerical Solution of Non-Isothermal Fluid Flows Using Local Radial Basis Functions (LRBF) Interpolation and a Velocity-Correction Method

by G. C. Bourantas¹, E. D. Skouras², V. C. Loukopoulos⁴

1 Department of Medical Physics, School of Medicine, University of Patras, GR 26500, Rion, Greece.
2 Department of Chemical Engineering, University of Patras, GR 26500, Rion, Greece.
3 Institute of Chemical Engineering and High Temperature Chemical Processes - Foundation for Research and Technology, P.O. Box 1414, GR-26504, Patras, Rion, Greece.
4 Department of Physics, University of Patras, Patras, 26500, Rion ,Greece.

Computer Modeling in Engineering & Sciences 2010, 64(2), 187-212. https://doi.org/10.3970/cmes.2010.064.187

Abstract

Meshfree point collocation method (MPCM) is developed, solving the velocity-vorticity formulation of Navier-Stokes equations, for two-dimensional, steady state incompressible viscous flow problems in the presence of heat transfer. Particular emphasis is placed on the application of the velocity-correction method, ensuring the continuity equation. The Gaussian Radial Basis Functions (GRBF) interpolation is employed to construct the shape functions in conjunction with the framework of the point collocation method. The cases of forced, natural and mixed convection in a 2D rectangular enclosure are examined. The accuracy and the stability of the proposed scheme are demonstrated through three representative, well known and established benchmark problems. Results are presented for high values of the characteristics non-dimensional numbers of the flow, that is, the Reynolds, the Rayleigh and the Richardson number.

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