Mai-Duy, Nam and Tran-Cong, Thanh (2010) A control volume technique based on integrated RBFNs for the convection-diffusion equation. Numerical Methods for Partial Differential Equations, 26 (2). 426 -447. ISSN 0749-159X
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Official URL: http://dx.doi.org/10.1002/num.20444
Identification Number or DOI: doi: 10.1002/num.20444
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.
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