TY - JOUR
T1 - Discrete finite volume formulation for multidimensional fragmentation equation and its convergence analysis
AU - Singh, Mehakpreet
AU - Matsoukas, Themis
AU - Ranade, Vivek
AU - Walker, Gavin
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/9/1
Y1 - 2022/9/1
N2 - 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.
AB - 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.
KW - Convergence analysis
KW - Finite volume scheme
KW - Integro-partial differential equation
KW - Monte Carlo method
KW - Multidimensional fragmentation
KW - Population dynamics
UR - http://www.scopus.com/inward/record.url?scp=85131365497&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2022.111368
DO - 10.1016/j.jcp.2022.111368
M3 - Article
AN - SCOPUS:85131365497
SN - 0021-9991
VL - 464
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 111368
ER -