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Discrete finite volume formulation for multidimensional fragmentation equation and its convergence analysis

Date
2022
Abstract
The present work is focused on developing a finite volume scheme for a multidimensional fragmentation equation. The finite volume scheme is established using the concept of overlapping of the cells whose mathematical formulation is both straightforward and robust on any kind of grid. The numerical development is further supported by thorough discussion of the mathematical analysis using Lipschitz condition and consistency of the method. The proposed finite volume scheme conserves the total mass in the system and is shown to estimate several other moments accurately, even though no special measure is taken to capture these moments. The testing of the proposed scheme is investigated against the constant number Monte Carlo method and exact benchmarking problems. The new scheme shows second order convergence on both uniform and nonuniform grids irrespective of the breakage kernel and selection function.
Supervisor
Description
Publisher
Elsevier
Citation
Journal of Computational Physics, 2022, 464, 111368
Collections
Chemical Sciences
Bernal Institute
School of Engineering
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Singh_2022_Discrete.pdf
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Keywords
multidimensional fragmentation, integro-partial differential equations, finite volume scheme, Monte Carlo method, population dynamics, convergence analysis, Chemical sciences, Engineering
ULRR Identifiers
https://doi.org/10.34961/researchrepository-ul.27242109
 https://researchrepository.ul.ie/handle/10344/13963
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Funding Information
Sustainable Development Goals
(6) Clean Water and Sanitation, (9) Industry, Innovation and Infrastructure
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Article
Rights
https://creativecommons.org/licenses/by-nc-sa/4.0/
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