Asymptotic models for free boundary flow in porous media
Analysis of PDEs
2019-08-15 v3 Fluid Dynamics
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.
Cite
@article{arxiv.1810.10756,
title = {Asymptotic models for free boundary flow in porous media},
author = {Rafael Granero-Belinchón and Stefano Scrobogna},
journal= {arXiv preprint arXiv:1810.10756},
year = {2019}
}