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Journal of Porous Media
インパクトファクター: 1.49 5年インパクトファクター: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN 印刷: 1091-028X
ISSN オンライン: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v17.i9.20
pages 763-784

WELL-POSEDNESS AND NUMERICAL SOLUTION OF A NONLINEAR VOLTERRA PARTIAL INTEGRO-DIFFERENTIAL EQUATION MODELING A SWELLING POROUS MATERIAL

Keith J. Wojciechowski
Department of Mathematics, Statistics, and Computer Science, University of Wisconsin−Stout, 202D Jarvis Hall Science Wing, 41010th Avenue East, Menomonie, WI54751-0790, USA
Jinhai Chen
Department of Mathematical and Statistical Sciences, University of Colorado−Denver, Campus Box 170, PO Box 173364, Denver, CO 80217-3364, USA
Lynn Schreyer-Bennethum
Department of Mathematical and Statistical Sciences, University of Colorado−Denver, Campus Box 170, PO Box 173364, Denver, CO 80217-3364, USA
Kristian Sandberg
Computational Solutions, Inc., 1800 30th St. Suite 210B, Boulder, CO 80301-1088, USA

要約

We mathematically analyze an initial-boundary value problem that involves a nonlinear Volterra partial integro-differential equation derived using hybrid mixture theory and used to model swelling porous materials where the application is an immersed, porous cylindrical material imbibing fluid through its exterior boundary. The model is written as an initial-boundary value problem and we establish well-posedness and numerically solve it using a novel approach to constructing pseudospectral differentiation matrices in a polar geometry. Numerical results are obtained and interpretations are provided for a small variety of diffusion and permeability coefficients and parameters to simulate the model's behavior and to demonstrate its viability as a model for swelling porous materials exhibiting viscoelastic behavior.