A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains

Abstract

This paper reports a new discretisation technique for the streamfunction-vorticity-temperature ($\psi - \omega - T$) formulation governing natural convection defined in 2D enclosured domains. The proposed technique combines strengths of three schemes, i.e. smooth discretisations (Galerkin formulation), powerful high-order approximations (one-dimensional integrated radial-basis-function networks) and pressure-free low-order system ($\psi-\omega-T$ formulation). In addition, a new effective way of deriving computational boundary conditions for the vorticity is proposed. Two benchmark test problems, namely free convection in a square slot and a concentric annulus, are considered, where a convergent solution for the former is achieved up to the Rayleigh number of 10/8.