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A Regularized Finite Volume Numerical Method for the Extended Porous Medium Equation Relevant to Moisture Dynamics with Evaporation in Non-woven Fibrous Sheets

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Model Design and Simulation Analysis (AsiaSim 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 603))

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Abstract

The extended porous medium equation (PME) is a degenerate nonlinear diffusion equation that effectively describes moisture dynamics with evaporation in non-woven fibrous sheets. We propose a new finite volume numerical model of the extended PME incorporating regularization of nonlinear degenerate terms, and apply it to test cases for verification of accuracy, stability, and versatility. One of the test cases considered is a new exact steady solution of the extended PME. We also examine a differential equation-based adaptive re-meshing technique for resolving sharp transitions of solution profiles that may be optionally incorporated into the procedure above. The computational results demonstrate satisfactory accuracy of the proposed numerical model, with reasonable reproduction of complicated moisture dynamics involving sharp transitions and divorce of supports.

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Acknowledgements

We thank Dr. Ichiro Kita and Dr. Kotaro Fukada in Faculty of Life and Environmental Science, Shimane University, Japan for providing helpful comments and suggestions on this article.

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Authors and Affiliations

  1. Faculty of Life and Environmental Science, Shimane University, Matsue, Japan

    Hidekazu Yoshioka

  2. Institute of Mathematics for Industry, Kyushu University - Australia Branch, La Trobe University, Melbourne, Australia

    Dimetre Triadis

Authors
  1. Hidekazu Yoshioka
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  2. Dimetre Triadis
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Correspondence to Hidekazu Yoshioka .

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Editors and Affiliations

  1. Korea Aerospace University , Goyang-si, Korea (Republic of)

    Syng Yup Ohn

  2. Korea Aerospace University , Goyang-si, Korea (Republic of)

    Sung Do Chi

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Yoshioka, H., Triadis, D. (2016). A Regularized Finite Volume Numerical Method for the Extended Porous Medium Equation Relevant to Moisture Dynamics with Evaporation in Non-woven Fibrous Sheets. In: Ohn, S., Chi, S. (eds) Model Design and Simulation Analysis. AsiaSim 2015. Communications in Computer and Information Science, vol 603. Springer, Singapore. https://doi.org/10.1007/978-981-10-2158-9_1

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  • DOI: https://doi.org/10.1007/978-981-10-2158-9_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2157-2

  • Online ISBN: 978-981-10-2158-9

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