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A comparative study of two different finite difference methods for solving advection–diffusion reaction equation for modeling exponential traveling wave in heat and mass transfer processes

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Abstract

An unconditionally-positive finite difference (UPFD) and the standard explicit finite difference schemes are compared to the analytical solution of the advection–diffusion reaction equation which describes the exponential traveling wave in heat and mass transfer processes. It is found that although the unconditional positivity of the UPFD scheme, this scheme is less accurate than the standard explicit finite difference scheme. This is because the UPFD scheme contains additional truncation-error terms in the approximations of the first and second derivatives with respect to x, which are evaluated at different moments in time. While these terms tend to zero as the mesh is refined, the UPFD scheme nevertheless remains less accurate than its standard explicit finite difference counterpart. The presented results are important when modeling a heat and mass transfer processes using the investigated advection–diffusion reaction equation. Furthermore, current and future developers of coupled multi-species transport models may draw on the ideas of solutions methods employed in this study to further develop numerical models for various types of coupled multi-species transport problems.

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Acknowledgements

The work described in this paper was supported by the Strategic Research Grant of City University of Hong Kong (Project No. CityU 7004600) and by a grant from Serbian Ministry of Education, Science and Technological Development (Agreement No. 451-03-68/2020-14/200122).

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Authors and Affiliations

  1. Faculty of Science, University of Kragujevac, R. Domanovića 12, Kragujevac, Serbia

    Svetislav Savović

  2. City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China

    Svetislav Savović & Alexandar Djordjevich

  3. University of Priština in Kosovska Mitrovica, Faculty of Sciences and Mathematics, Kosovska Mitrovica, Serbia

    Branko Drljača

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  1. Svetislav Savović
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  2. Branko Drljača
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  3. Alexandar Djordjevich
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Correspondence to Svetislav Savović.

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Savović, S., Drljača, B. & Djordjevich, A. A comparative study of two different finite difference methods for solving advection–diffusion reaction equation for modeling exponential traveling wave in heat and mass transfer processes. Ricerche mat 71, 245–252 (2022). https://doi.org/10.1007/s11587-021-00665-2

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  • DOI: https://doi.org/10.1007/s11587-021-00665-2

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