Journal Title
Title of Journal: J Sci Comput
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Abbravation: Journal of Scientific Computing
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Authors: J H M ten Thije Boonkkamp M J H Anthonissen
Publish Date: 2010/06/16
Volume: 46, Issue: 1, Pages: 47-70
Abstract
We present a new finite volume scheme for the advectiondiffusionreaction equation The scheme is second order accurate in the grid size both for dominant diffusion and dominant advection and has only a threepoint coupling in each spatial direction Our scheme is based on a new integral representation for the flux of the onedimensional advectiondiffusionreaction equation which is derived from the solution of a local boundary value problem for the entire equation including the source term The flux therefore consists of two parts corresponding to the homogeneous and particular solution of the boundary value problem Applying suitable quadrature rules to the integral representation gives the complete flux scheme Extensions of the complete flux scheme to twodimensional and timedependent problems are derived containing the cross flux term or the time derivative in the inhomogeneous flux respectively The resulting finite volumecomplete flux scheme is validated for several test problemsThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team
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