The Meshfree Finite Volume Method with application to multi-phase porous media models

Abstract : Numerical methods form a cornerstone of the analysis and investigation of mathematical models for physical processes. Many classical numerical schemes rely on the application of strict meshing structures to generate accurate solutions, which in some applications are an infeasible constraint. Within this paper we outline a new meshfree numerical scheme, which we call the Meshfree Finite Volume Method (MFVM). The MFVM uses interpolants to approximate fluxes in a disjoint finite volume scheme, allowing for the accurate solution of strong-form PDEs. We present a derivation of the MFVM, and give error bounds on the spatial and temporal approximations used within the scheme. We present a wide variety of applications of the method, showing key features, and advantages over traditional meshed techniques. We close with an application of the method to a non-linear multi-phase wood drying model, showing the potential for solving numerically challenging problems.
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Article dans une revue
Journal of Computational Physics, Elsevier, 2017, 333, pp.369 - 386. 〈10.1016/j.jcp.2016.12.045〉
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Soumis le : jeudi 30 novembre 2017 - 14:32:49
Dernière modification le : jeudi 5 avril 2018 - 12:30:10

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Brody Foy, Patrick Perre, Ian Turner. The Meshfree Finite Volume Method with application to multi-phase porous media models. Journal of Computational Physics, Elsevier, 2017, 333, pp.369 - 386. 〈10.1016/j.jcp.2016.12.045〉. 〈hal-01652602〉

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