Open Access

ARTICLE

A Radial Basis Function Collocation Approach in Computational Fluid Dynamics

B. Šarler¹

1 Laboratory for Multiphase Processes, Nova Gorica Polytechnic, Nova Gorica, Slovenia.

Computer Modeling in Engineering & Sciences 2005, 7(2), 185-194. https://doi.org/10.3970/cmes.2005.007.185

Abstract

This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primitive variable solution procedure for the coupled mass, momentum, and energy transport representing the natural convection in an incompressible Newtonian Bussinesq fluid are elaborated. A comparison of different collocation strategies is performed based on the two dimensional De Vahl Davis steady natural convection benchmark with Prandtl number Pr = 0.71, and Rayleigh numbers Ra = 10³, 10⁴, 10⁵, 10⁶. Multiquadrics radial basis functions are used. The three methods are assessed in terms of streamfunction extreme, cavity Nusselt number, and mid-plane velocity components. Best performance is achieved with the modified approach.

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Keywords

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