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A control volume technique based on integrated RBFNs for the convection–diffusion equation
Author(s) -
MaiDuy N.,
TranCong T.
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20444
Subject(s) - control volume , mathematics , discretization , benchmark (surveying) , convergence (economics) , convection–diffusion equation , diffusion , mathematical analysis , flow (mathematics) , nonlinear system , finite volume method , mechanics , geometry , thermodynamics , physics , geodesy , quantum mechanics , economic growth , economics , geography
This article reports a new high‐order control‐volume discretization 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. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010