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Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

Author

Listed:
  • Jitraj Saha

    (Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli 620 015, Tamil Nadu, India)

  • Andreas Bück

    (Institute of Particle Technology (LFG), Friedrich-Alexander University Erlangen-Nürnberg, D-91058 Erlangen, Germany)

Abstract

In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems.

Suggested Citation

  • Jitraj Saha & Andreas Bück, 2021. "Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems," Mathematics, MDPI, vol. 9(6), pages 1-27, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:635-:d:518684
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    Cited by:

    1. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.

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