Mathematical analysis of finite volume preserving scheme for nonlinear Smoluchowski equation

Mehakpreet Singh, Themis Matsoukas, Gavin Walker

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number132221
JournalPhysica D: Nonlinear Phenomena
DOIs
StateAccepted/In press - Jan 1 2019

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Smoluchowski Equation
applications of mathematics
Coalescence
Mathematical Analysis
Finite Volume
Nonlinear equations
preserving
nonlinear equations
Nonlinear Equations
Finite Volume Scheme
Order of Convergence
kernel
Bins
coalescing
Agglomeration
Convergence Analysis
Overlapping
Aggregation
Grid
grids

All Science Journal Classification (ASJC) codes

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

Cite this

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

In: Physica D: Nonlinear Phenomena, 01.01.2019.

Research output: Contribution to journalArticle

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