Radial basis function-enhanced domain-free discretization method and its applications

Abstract

The recently proposed domain-free discretization (DFD) method is based on the Lagrange interpolation and polynomial-based differential quadrature (PDQ) method. In this article, the radial basis function (RBF) approximation is used in the DFD method as the interpolation scheme for function approximation, and the RBF-DQ method is applied to derivative approximation. The new variant of DFD method is then applied to simulation of natural convection in both concentric and eccentric annuli between inner circular and outer square cylinders. It is found from the numerical examples that the usage of radial basis function can greatly enhance the DFD method in terms of the computational stability and convergence speed.