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A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition

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  • Maria Laura Martins-Costa
  • Daniel Cunha da Silva
  • Michele Cunha da Silva
  • Rogério Martins Saldanha da Gama

Abstract

The present work proposes an adequate constitutive relation to treat the process of filling with a fluid porous medium. This relation assures the problem to remain hyperbolic when the porous medium is saturated by the fluid. When the fluid fraction reaches porosity, the proposed constitutive relation increases the porous matrix resistance to more fluid inlet due to an important feature: it is a continuous and differentiable function with first derivative being also an increasing function. This allows assuring that the fluid fraction may exceed the porosity only by a very small value, making the constitutive relation realistic. Some examples compare this new constitutive relation with previous ones, highlighting its advantages.

Suggested Citation

  • Maria Laura Martins-Costa & Daniel Cunha da Silva & Michele Cunha da Silva & Rogério Martins Saldanha da Gama, 2019. "A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:2347809
    DOI: 10.1155/2019/2347809
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