On the numerical solution of a variable-coefficient Burgers equation arising in granular segregation

We study a variable-coefficient Burgers equation arising in the modelling of segregation of dry bidisperse granular mixtures. The equation is subject to nonlinear boundary conditions for the particle flux. We construct a strongly implicit Crank--Nicolson type of numerical scheme for the latter equat...

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Bibliographic Details
Published inarXiv.org
Main Author Christov, Ivan C
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.12.2017
Subjects
Boundary conditions
Burgers equation
Coefficients
Computer simulation
Mathematical analysis
Mathematical models
Physics - Computational Physics
Physics - Soft Condensed Matter
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ISSN2331-8422
DOI10.48550/arxiv.1707.00034

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Summary:We study a variable-coefficient Burgers equation arising in the modelling of segregation of dry bidisperse granular mixtures. The equation is subject to nonlinear boundary conditions for the particle flux. We construct a strongly implicit Crank--Nicolson type of numerical scheme for the latter equation. The scheme is benchmarked against a standard exact solution of kink type, showing second-order of accuracy and good discrete conservation properties. Two segregation problems considered in the literature are then solved and discussed. The first is the case of a linear kinetic stress profile, which renders the governing equation of constant-coefficient type, while the second is the case of a variable kinetic stress profile based on an expression fit to particle dynamics simulation data.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1707.00034