Discretization and parallel iterative schemes for advection-diffusion-reaction problems

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Conservation laws of advection-diffusion-reaction (ADR) type are ubiquitous in continuum physics. In this paper we outline discretization of these problems and iterative schemes for the resulting linear system. For discretization we use the finite volume method in combination with the complete flux scheme. The numerical flux is the superposition of a homogeneous flux, corresponding to the advection-diffusion operator, and the inhomogeneous flux, taking into account the effect of the source term (ten Thije Boonkkamp and Anthonissen, J Sci Comput 46(1):47–70, 2011). For a three-dimensional conservation law this results in a 27-point coupling for the unknown as well as the source term. Direct solution of the sparse linear systems that arise in 3D ADR problems is not feasible due to fill-in. Iterative solution of such linear systems remains to be the only efficient alternative which requires less memory and shorter time to solution compared to direct solvers. Iterative solvers require a preconditioner to reduce the number of iterations. We present results using several different preconditioning techniques and study their effectiveness.

Originele taal-2Engels
TitelNumerical Mathematics and Advanced Applications ENUMATH 2015
RedacteurenB. Karasözen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe, Ö. Uğur
Plaats van productieDordrecht
Aantal pagina's9
ISBN van elektronische versie978-3-319-39929-4
ISBN van geprinte versie978-3-319-39927-0
StatusGepubliceerd - 2016
Evenement2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015) - Middle East Technical University, Ankara, Turkije
Duur: 14 sep 201518 sep 2015

Publicatie series

NaamLecture Notes in Computational Science and Engineering
ISSN van geprinte versie14397358


Congres2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015)
Verkorte titelENUMATH 2015

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