A Newton type linearization based two grid method for coupling fluid flow with porous media flow

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• 作者：Peiqi Huang^a ; ¹ ; ^{pqhuang@njfu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Mingchao Cai^b ; ^{cmchao2005@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Feng Wang^c ; ² ; ^{fwang@njnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Finite element ; Decoupling ; Linearization ; Navier&ndash ; Stokes/Darcy model ; Two-grid method
• 刊名：Applied Numerical Mathematics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：106
• 期：Complete
• 页码：182-198
• 全文大小：585 K

文摘

In this paper, we propose a two-grid finite element method for solving the mixed Navier–Stokes/Darcy model with the Beavers–Joseph–Saffman interface condition. After solving a coupled nonlinear problem on a coarse grid, we sequentially solve decoupled and linearized subproblems on a fine grid and then correct the solution on the same grid. Compared with the existing work on the two-grid methods for the coupled model, our two-grid method allows a much higher order scaling between the coarse grid size H and the fine grid size h. Specifically, if a k  -th order discretization is applied, by using $h=H^{\frac{2k+1}{k}}$ for k=1,2$k=1,2$ and $h=H^{\frac{k+1}{k-1}}$ for k≥3$k\ge 3$, the final step two-grid solution errors in the energy norm are still optimal. Numerical experiments are also given to confirm the theoretical analysis.