Discrete Finite Volume Formulation for Multidimensional Fragmentation Equation and its Convergence Analysis

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 formu- lation 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.

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Work Title Discrete Finite Volume Formulation for Multidimensional Fragmentation Equation and its Convergence Analysis
Access
Open Access
Creators
  1. Mehakpreet Singh
  2. Themis Matsoukas
  3. Vivek Ranade
  4. Gavin Walker
Keyword
  1. Multidimensional fragmentation
  2. Integro-partial differential equation
  3. Finite volume scheme
  4. Monte Carlo method
  5. Population dynamics
  6. Convergence analysis
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Acknowledgments
  1. The authors gratefully acknowledge the financial support provided by Marie Sklodowska-Curie Individual Fellowship no. 841906 to Dr. Mehakpreet Singh.
Publisher
  1. Elsevier
Publication Date June 2, 2022
Publisher Identifier (DOI)
  1. doi.org/10.1016/j.jcp.2022.111368
Related URLs
Deposited June 02, 2022

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Version 1
published

  • Created
  • Updated
  • Updated
  • Updated Acknowledgments Show Changes
    Acknowledgments
    • The authors gratefully acknowledge the financial support provided by Marie Sk􏰯lodowska-Curie Individual Fellowship no. 841906 to Dr. Mehakpreet Singh.
  • Added Creator Mehakpreet. Singh
  • Added Creator Mehakpreet. Singh
  • Added Creator Vivek Ranade
  • Added Creator Gavin Walker
  • Added Manuscript.pdf
  • Updated License Show Changes
    License
    • https://creativecommons.org/licenses/by-nc-nd/4.0/
  • Published
  • Updated Keyword, Description, Publication Date Show Changes
    Keyword
    • Multidimensional fragmentation, Integro-partial differential equation, Finite volume scheme, Monte Carlo method, Population dynamics, Convergence analysis
    Description
    • 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 formu- lation 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.
    Publication Date
    • 2022-07-02
    • 2022-06-02
  • Renamed Creator Mehakpreet Singh Show Changes
    • Mehakpreet. Singh
    • Mehakpreet Singh
  • Renamed Creator Themis Matsoukas Show Changes
    • Mehakpreet. Singh
    • Themis Matsoukas
  • Updated Acknowledgments Show Changes
    Acknowledgments
    • The authors gratefully acknowledge the financial support provided by Marie Sk􏰯lodowska-Curie Individual Fellowship no. 841906 to Dr. Mehakpreet Singh.
    • The authors gratefully acknowledge the financial support provided by Marie Sklodowska-Curie Individual Fellowship no. 841906 to Dr. Mehakpreet Singh.
  • Updated