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

Mehakpreet Singh, Themis Matsoukas, Vivek Ranade, Gavin Walker

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish (US)
Article number111368
JournalJournal of Computational Physics
Volume464
DOIs
StatePublished - Sep 1 2022

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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