A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

Pasdunkorale Arachchige, Jayantha & Pettet, Graeme J. (2014) A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems. Applied Mathematics and Computation, 231, pp. 445-462.

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The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature.

Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models.

This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest.

The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

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ID Code: 68146
Item Type: Journal Article
Refereed: Yes
Keywords: Nonlinear, Reaction, Advection, Diffusion, Shock, Chemotaxis, Finite volume method
DOI: 10.1016/j.amc.2013.12.179
ISSN: 0096-3003
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical and Computational Mathematics not elsewhere classified (010399)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, [VOL 231, (2014)] DOI: 10.1016/j.amc.2013.12.179
Deposited On: 10 Mar 2014 00:26
Last Modified: 23 Mar 2016 03:50

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