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A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

Carr, Elliot Joseph, Turner, Ian, & Perré, Patrick (2012) A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying. Journal of Computational Physics, 233, pp. 66-82.

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    Abstract

    A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

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    1 citations in Scopus
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    ID Code: 54158
    Item Type: Journal Article
    Keywords: exponential integrators, exponential Rosenbrock-type methods, variable-stepsize implementation, matrix function approximation, Krylov subspace methods, heterogeneous porous media, heat and mass transfer, drying, wood
    DOI: 10.1016/j.jcp.2012.07.024
    ISSN: 0021-9991
    Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
    Divisions: Current > Schools > School of Mathematical Sciences
    Current > QUT Faculties and Divisions > Science & Engineering Faculty
    Copyright Owner: Copyright 2012 Elsevier
    Copyright Statement: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.
    Deposited On: 16 Oct 2012 16:46
    Last Modified: 18 Mar 2013 13:04

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