A Radial Basis Function Collocation Approach in Computational Fluid Dynamics

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. keyword: radial basis function collocation method, heat transfer, fluid flow, natural convection.