×

A radial basis function collocation approach in computational fluid dynamics. (English) Zbl 1189.76380

Summary: 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 Boussinesq 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 \(\text{Ra}= 10^3, 10^4, 10^5, 10^6\). 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.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)