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A Linearity Preserving Algebraic Flux Correction Scheme of Upwind Type Satisfying the Discrete Maximum Principle on Arbitrary Meshes

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Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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Abstract

Various choices of limiters in the framework of algebraic flux correction (AFC) schemes applied to the numerical solution of scalar steady-state convection–diffusion–reaction equations are discussed. A new limiter of upwind type is proposed for which the AFC scheme satisfies the discrete maximum principle and linearity preservation property on arbitrary meshes.

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References

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Acknowledgements

This work has been supported through the grant No. 16-03230S of the Czech Science Foundation.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Numerical Mathematics, Charles University, Prague, Czech Republic

    Petr Knobloch

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  1. Petr Knobloch
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Correspondence to Petr Knobloch .

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Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Knobloch, P. (2019). A Linearity Preserving Algebraic Flux Correction Scheme of Upwind Type Satisfying the Discrete Maximum Principle on Arbitrary Meshes. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_86

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