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

  • Hidekazu YoshiokaEmail author
  • Dimetre Triadis
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 603)


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.


Moisture dynamics Evaporation Non-woven fibrous sheet Extended porous medium equation Dual-finite volume method 



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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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Faculty of Life and Environmental ScienceShimane UniversityMatsueJapan
  2. 2.Institute of Mathematics for Industry, Kyushu University - Australia BranchLa Trobe UniversityMelbourneAustralia

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