On Unconditionally Positivity Preserving and Conservative Methods for Systems of Advection-Diffusion-Reaction Equations

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Wallbaum_GAMM2014.pdf (307.46 KB)

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https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201410463

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https://doi.org/10.1002/pamm.201410463
 http://hdl.handle.net/11603/39773

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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Author/Creator ORCID

https://orcid.org/0000-0003-1745-2292

Date

2014-12-22

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journal articles
preprints
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Citation of Original Publication

Gobbert, Matthias K., Andreas Meister, and Sven Wallbaum. “On Unconditionally Positivity Preserving and Conservative Methods for Systems of Advection-Diffusion-Reaction Equations.” PAMM 14, no. 1 (2014): 965–66. https://doi.org/10.1002/pamm.201410463.

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This is the pre-peer reviewed version of the following article: Gobbert, Matthias K., Andreas Meister, and Sven Wallbaum. “On Unconditionally Positivity Preserving and Conservative Methods for Systems of Advection-Diffusion-Reaction Equations.” PAMM 14, no. 1 (2014): 965–66. https://doi.org/10.1002/pamm.201410463., which has been published in final form at https://doi.org/10.1002/pamm.201410463. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions

Subjects

Abstract

An unconditionally positivity preserving finite difference scheme (UPFD) for systems of advection-diffusion-reaction equations with non-linear reaction terms is proposed. A modified Patankar approach is employed with respect to the reaction part in order to ensure both conservativity and positivity without any additional constraints on the time step size. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)