A Newton type linearization based two grid method for coupling fluid flow with porous media flow
A Newton type linearization based two grid method for coupling fluid flow with porous media flow
复制标题
基于牛顿型线性化的流体流动与多孔介质流动耦合的二网格法
DOI：
10.1016/j.apnum.2016.04.003
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发表时间：
2016
影响因子：
2.8
通讯作者：
Wang Feng
中科院分区：
文献类型：
--
作者：
Huang Peiqi;Cai Mingchao;Wang Feng
本文提出了一种求解具有Beivers-Joseph-Saffman界面条件的混合Navier-Stokes/Darcy模型的两网格法。在粗网格上求解耦合非线性问题后，在细网格上依次求解解耦和线性化的子问题，然后在同一网格上对解进行修正。与已有的耦合模式二次网格方法相比，我们的两次网格方法允许在粗网格尺寸和精细网格尺寸h之间进行高得多的阶缩放。具体地说，如果采用k阶离散化，通过使用h=H^[(2k+1)/k](k=1，2)和h=H^[(k+1)/(k−1)](k≥3)，最后一步两网格解的能量范数误差为
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 Hand the fine grid size h. Specifically, if a k-th order discretization is applied, by using h =H^[(2k+1)/k] for k =1, 2 and h =H^[(k+1)/(k−1)]for k ≥3, the final step two-grid solution errors in the energy norm are