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Volume 9
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10.3390/math9060635
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Article

Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

by
Jitraj Saha
1 and
Andreas Bück
2,*
1
Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli 620 015, Tamil Nadu, India
2
Institute of Particle Technology (LFG), Friedrich-Alexander University Erlangen-Nürnberg, D-91058 Erlangen, Germany
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(6), 635; https://doi.org/10.3390/math9060635
Submission received: 8 February 2021 / Revised: 8 March 2021 / Accepted: 9 March 2021 / Published: 17 March 2021
(This article belongs to the Special Issue Mathematical Methods, Modelling and Applications)
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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.
Keywords: conservative formulation; multidimensional fragmentation equation; weight functions; finite volume scheme conservative formulation; multidimensional fragmentation equation; weight functions; finite volume scheme

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MDPI and ACS Style

Saha, J.; Bück, A. Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems. Mathematics 2021, 9, 635. https://doi.org/10.3390/math9060635

AMA Style

Saha J, Bück A. Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems. Mathematics. 2021; 9(6):635. https://doi.org/10.3390/math9060635

Chicago/Turabian Style

Saha, Jitraj, and Andreas Bück. 2021. "Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems" Mathematics 9, no. 6: 635. https://doi.org/10.3390/math9060635

APA Style

Saha, J., & Bück, A. (2021). Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems. Mathematics, 9(6), 635. https://doi.org/10.3390/math9060635

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