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The difference between semi-continuum model and Richards' equation for unsaturated porous media flow.


ABSTRACT: Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the retention curve of each block scales with the block size and in the limit becomes a hysteresis operator of the Prandtl-type used in elasto-plasticity models. Mathematical analysis showed that the limit of the semi-continuum model is a hyperbolic-parabolic partial differential equation with a hysteresis operator of Prandl's type. This limit differs from the standard Richards' equation, which is a parabolic equation and is not able to describe finger-like flow.

SUBMITTER: Vodak R 

PROVIDER: S-EPMC9090790 | biostudies-literature | 2022 May

REPOSITORIES: biostudies-literature

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The difference between semi-continuum model and Richards' equation for unsaturated porous media flow.

Vodák Rostislav R   Fürst Tomáš T   Šír Miloslav M   Kmec Jakub J  

Scientific reports 20220510 1


Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the  ...[more]

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