Asymptotic models for free boundary flow in porous media
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2019-05Derechos
© <2019>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Publicado en
Physica D: Nonlinear Phenomena, Volume 392, Pages 1-16
Editorial
Elsevier
Enlace a la publicación
Palabras clave
Muskat problem
Darcy law
Forchheimer flow
Moving interfaces
Free-boundary problems
Resumen/Abstract
We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to be very small. The models we derive capture the nonlinear interaction of the original free boundary Darcy and Forchheimer problem up to quadratic terms. Furthermore, we provide models that consider both the two-dimensional and three-dimensional cases, with and without bottom topography.
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