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A complete flux scheme for the stationary advection‐diffusion‐reaction equation
Author(s) -
ten Thije Boonkkamp J.H.M.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700317
Subject(s) - advection , conservation law , cartesian coordinate system , finite volume method , convection–diffusion equation , péclet number , flux (metallurgy) , diffusion , numerical diffusion , mathematics , mathematical analysis , order (exchange) , scheme (mathematics) , reaction–diffusion system , physics , mechanics , geometry , thermodynamics , chemistry , organic chemistry , finance , economics
Expressions for the numerical flux of a conservation law of advection‐diffusion‐reaction type are derived from a local solution of the entire conservation law, including the source term. The resulting complete flux scheme is given for one‐dimensional (in Cartesian and spherical coordinates) and two‐dimensional model equations. Combined with a finite volume method, the numerical scheme is second order accurate, uniformly in the Peclet numbers. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)