### Abstract

This study presents the convergence analysis of the recently developed finite volume preserving scheme (Forestier-Coste and Mancini, 2012) for approximating a coalescence or Smoluchowski equation. The idea of the finite volume scheme is to preserve the total volume in the system by modifying the coalescence kernel using the notion of overlapping bins (cells). The consistency of the finite volume scheme is examined thoroughly in order to prove second-order convergence on uniform, non-uniform smooth and locally uniform grids independently of the aggregation kernel. The theoretical observations of order of convergence is verified using the experimental order of convergence for analytically tractable kernels.

Original language | English (US) |
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Article number | 132221 |

Journal | Physica D: Nonlinear Phenomena |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics

### Cite this

*Physica D: Nonlinear Phenomena*, [132221]. https://doi.org/10.1016/j.physd.2019.132221

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**Mathematical analysis of finite volume preserving scheme for nonlinear Smoluchowski equation.** / Singh, Mehakpreet; Matsoukas, Themis; Walker, Gavin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Mathematical analysis of finite volume preserving scheme for nonlinear Smoluchowski equation

AU - Singh, Mehakpreet

AU - Matsoukas, Themis

AU - Walker, Gavin

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This study presents the convergence analysis of the recently developed finite volume preserving scheme (Forestier-Coste and Mancini, 2012) for approximating a coalescence or Smoluchowski equation. The idea of the finite volume scheme is to preserve the total volume in the system by modifying the coalescence kernel using the notion of overlapping bins (cells). The consistency of the finite volume scheme is examined thoroughly in order to prove second-order convergence on uniform, non-uniform smooth and locally uniform grids independently of the aggregation kernel. The theoretical observations of order of convergence is verified using the experimental order of convergence for analytically tractable kernels.

AB - This study presents the convergence analysis of the recently developed finite volume preserving scheme (Forestier-Coste and Mancini, 2012) for approximating a coalescence or Smoluchowski equation. The idea of the finite volume scheme is to preserve the total volume in the system by modifying the coalescence kernel using the notion of overlapping bins (cells). The consistency of the finite volume scheme is examined thoroughly in order to prove second-order convergence on uniform, non-uniform smooth and locally uniform grids independently of the aggregation kernel. The theoretical observations of order of convergence is verified using the experimental order of convergence for analytically tractable kernels.

UR - http://www.scopus.com/inward/record.url?scp=85074160732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074160732&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2019.132221

DO - 10.1016/j.physd.2019.132221

M3 - Article

AN - SCOPUS:85074160732

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

M1 - 132221

ER -