Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

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 i...

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Main Authors: Jitraj Saha, Andreas Bück
Format: Article
Language:English
Published: MDPI AG 2021-03-01
Series:Mathematics
Subjects:
conservative formulation
multidimensional fragmentation equation
weight functions
finite volume scheme
Online Access:https://www.mdpi.com/2227-7390/9/6/635
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spelling doaj-f3662fd08a2c45789a85dc5e3ccbed1c2021-03-18T00:00:42ZengMDPI AGMathematics2227-73902021-03-01963563510.3390/math9060635Conservative Finite Volume Schemes for Multidimensional Fragmentation ProblemsJitraj Saha0Andreas Bück1Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli 620 015, Tamil Nadu, IndiaInstitute of Particle Technology (LFG), Friedrich-Alexander University Erlangen-Nürnberg, D-91058 Erlangen, GermanyIn 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.https://www.mdpi.com/2227-7390/9/6/635conservative formulationmultidimensional fragmentation equationweight functionsfinite volume scheme
collection DOAJ
language English
format Article
sources DOAJ
author Jitraj Saha
Andreas Bück
spellingShingle Jitraj Saha
Andreas Bück
Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems
Mathematics
conservative formulation
multidimensional fragmentation equation
weight functions
finite volume scheme
author_facet Jitraj Saha
Andreas Bück
author_sort Jitraj Saha
title Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems
title_short Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems
title_full Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems
title_fullStr Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems
title_full_unstemmed Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems
title_sort conservative finite volume schemes for multidimensional fragmentation problems
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-03-01
description 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.
topic conservative formulation
multidimensional fragmentation equation
weight functions
finite volume scheme
url https://www.mdpi.com/2227-7390/9/6/635
work_keys_str_mv AT jitrajsaha conservativefinitevolumeschemesformultidimensionalfragmentationproblems
AT andreasbuck conservativefinitevolumeschemesformultidimensionalfragmentationproblems
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