Radial-basis-function Calculations of Buoyancy-driven Flow in Concentric and Eccentric Annuli

摘要

This paper is concerned with the application of integrated radial-basis-function networks (IRBFNs) for the simulation of natural convection in concentric and eccentric annuli. Important features of the present technique include: (i) Taking a stream function - temperature formulation as the governing equations; (ii) Employing a Cartesian grid to discretize the problem domain; (iii) Using one-dimensional RBF approximations to represent the approximate solution; and (iv) Constructing the approximations through integration. These features result in an efficient numerical scheme as (i) the number of the governing differential equations is reduced from 4 to 2, (ii) the preprocessing is simple, (iii) the associated matrices have condition numbers in 2-norm that are much lower than those yielded through conventional RBF techniques, and (iv) the reduction of convergence rate caused by differentiation is avoided. A wide range of the Rayleigh number is considered. Results obtained are compared well with available numerical data in literature. Keywords: Natural convection; Cartesian grid method; Irregular domain; Integrated radial basis function networks