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A NEW CONSTRAINED CONSTITUTIVE EQUATION FOR UNSATURATED FLOWS OF INCOMPRESSIBLE LIQUIDS THROUGH RIGID POROUS MEDIA

Volume 14, Issue 3, 2011, pp. 205-217
DOI: 10.1615/JPorMedia.v14.i3.20
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ABSTRACT

This article proposes a new constitutive model for the partial pressure in unsaturated flows of incompressible liquids through rigid porous media. This constitutive equation for the pressure gives rise to a mathematical description in which the geometrical bound, representing the rigid porous medium assumption, is naturally taken into account—so that only physically meaningful solutions are allowed. A mixture theory approach describes the flow by considering three overlapping continuous constituents, representing the porous matrix (solid constituent), the fluid (liquid constituent), and an inert gas included to account for the compressibility of the mixture as a whole. Examples of Riemann problem solutions showing connections by rarefactions and shocks for both the classical model and the proposed constitutive approach for the partial pressure support the latter.

CITED BY
  1. Saldanha da Gama R.M., Pedrosa Filho J.J., Martins-Costa M.L., Modeling the saturation process of flows through rigid porous media by the solution of a nonlinear hyperbolic system with one constrained unknown, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 92, 11-12, 2012. Crossref

  2. Martins-Costa Maria Laura, Alegre Dario Monte, de Freitas Rachid Felipe Bastos, Jardim Luiz Guilherme C.M., Saldanha da Gama Rogério M., A hyperbolic mathematical modeling for describing the transition saturated/unsaturated in a rigid porous medium, International Journal of Non-Linear Mechanics, 95, 2017. Crossref

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