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A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

Dargaville, Steven & Farrell, Troy W. (2015) A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations. Journal of Computational and Applied Mathematics, 273, pp. 255-244.

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    Abstract

    A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

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    ID Code: 53398
    Item Type: Journal Article
    Additional URLs:
    Keywords: Cahn-Hilliard, finite volume, lithium iron phosphate, least squares
    DOI: 10.1016/j.cam.2014.06.020
    ISSN: 0377-0427
    Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
    Divisions: Current > Schools > School of Mathematical Sciences
    Current > QUT Faculties and Divisions > Science & Engineering Faculty
    Copyright Owner: Copyright 2014 Elsevier
    Deposited On: 30 Aug 2012 13:03
    Last Modified: 22 Aug 2014 23:19

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