Research On Finite Element Method For The Coupling Problem Of Incompressible Flow And Porous Medium Flow

In this article,we study the coupling problem of incompressible flow and porous media flow.The problem is mainly simulated by Navier-Stokes/Darcy model and Stokes/Darcy model.Based on the theory analysis of finite element method,this pa-per constructs the two-level method for the steady-state Navier-Stokes/Darcy model and the rotational pressure-correction method with modular grad-div stabilization for the time-dependent Stokes/Darcy model.Firstly,a two-level finite element method based on the Newton iterative method is proposed for solving the Navier-Stokes/Darcy model.The algorithm solves a nonlinear system on a coarse mesh H and two linearized problems of different loads on a fine mesh h=O(H4-?).Compared with the common two-grid finite element methods for the considered problem,the presented two-level method allows for larger scaling between the coarse and fine meshes,and can achieve better accuracy after scaling.Moreover,we prove the stability and convergence of the considered two-level method.Finally,we provide numerical experiment to exhibit the effectiveness of the presented method.Secondly,based on the idea of rotational pressure-correction method and mod-ular grad-div stabilization method,we construct a rotational pressure-correction method with the modular grad-div stabilization for the time-dependent Stokes/Darcy model.It can not only improve the efficiency of calculation but also the mass con-servation.In addition,we give the theoretical analysis of the unconditional stability of the presented method.Finally,the theoretical results are verified by numerical experiments and the merit of adding grad-div stabilization terms is manifested.