A control volume technique based on integrated RBFNs for the convection-diffusion equation

Abstract

This paper reports a new high-order control-volume discretisation for the convection-diffusion equation in one and two dimensions. Diffusive fluxes at the faces of a control volume and other terms embracing the unknown field variable are all approximated using one-dimensional integrated radial-basis-function networks; line integrals involving these fluxes and other integrals are evaluated using a high-order numerical integration scheme. The accuracy of the proposed technique is investigated numerically through the solution of several linear and nonlinear test problems, including a benchmark thermally-driven cavity flow. High-order convergence solutions are obtained.