@Article{AAMM-13-1418,
author = {Bian , HuanyingShen , Yedan and Hu , Guanghui},
title = {An $h$-Adaptive Finite Element Solution of the Relaxation Non-Equilibrium Model for Gravity-Driven Fingers},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2021},
volume = {13},
number = {6},
pages = {1418--1440},
abstract = {<p style="text-align: justify;">The study on the fingering phenomenon has been playing an important role in understanding the mechanism of the fluid flow through the porous media. In this paper, a numerical method consisting of the Crank-Nicolson scheme for the temporal discretization and the finite element method for the spatial discretization is proposed for the relaxation non-equilibrium Richards equation in simulating the fingering phenomenon. Towards the efficiency and accuracy of the numerical simulations, a predictor-corrector process is used for resolving the nonlinearity of the equation, and an $h$-adaptive mesh method is introduced for accurately resolving the solution around the wetting front region, in which a heuristic a posteriori error indicator is designed for the purpose. In numerical simulations, a traveling wave solution of the governing equation is derived for checking the numerical convergence of the proposed method. The effectiveness of the $h$-adaptive method is also successfully demonstrated by numerical experiments. Finally the&nbsp;mechanism on generating fingers is discussed by numerically studying several examples.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2020-0218},
url = {http://global-sci.org/intro/article_detail/aamm/19429.html}
}