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 sche...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.展开更多
基金supported by FDCT of Macao SAR(FDCT 029/2016/A1),MYRG of University of Macao(MYRG2017-00189-FST,MYRG2019-00154-FST)National Natural Science Foundation of China(Grant Nos.11922120,11871489,and 11401608)Department of Science and Technology of Guangdong Province.
文摘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.
