An $h$-Adaptive Finite Element Solution of the Relaxation Non-Equilibrium Model for Gravity-Driven Fingers
Year: 2021
Author: Huanying Bian, Yedan Shen, Guanghui Hu
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1418–1440
Abstract
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 mechanism on generating fingers is discussed by numerically studying several examples.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0218
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1418–1440
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Non-equilibrium Richard equation $h$-adaptive mesh method a posteriori error estimation fingering phenomenon porous media flow.