Asymptotic models for free boundary flow in porous media

PHYSICA D-NONLINEAR PHENOMENA

卷:392

Article

Granero-Belinchon, Rafael¹  Scrobogna, Stefano² 

[1] Univ Cantabria, Dept Matemat Estadist & Computac, Avda Los Castros S-N, Santander, Spain

[2] Basque Ctr Appl Math, Mazarredo 14, Bilbao, Spain

关键词: Muskat problem;    Darcy law;    Forchheimer flow;    Moving interfaces;    Free-boundary problems;   

DOI  :  10.1016/j.physd.2019.02.013

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free