| 非定常Navier-Stokes方程基于两重网格离散的有限元并行算法 |
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| 引用本文： | 丁琪,尚月强. 非定常Navier-Stokes方程基于两重网格离散的有限元并行算法[J]. 计算物理, 2020, 37(1): 10-18. DOI: 10.19596/j.cnki.1001-246x.8000 |
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| 作者姓名： | 丁琪 尚月强 |
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| 作者单位： | 西南大学数学与统计学院, 重庆 400715 |
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| 基金项目： | 重庆市基础与前沿探索研究计划项目;国家自然科学基金;中央高校基本科研业务费专项 |
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| 摘 要： | 基于两重网格离散和区域分解技巧，提出三种求解非定常Navier-Stokes方程的有限元并行算法.算法的基本思想是在每一时间迭代步，在粗网格上采用Oseen迭代法求解非线性问题，在细网格上分别并行求解Oseen、Newton、Stokes线性问题以校正粗网格解.对于空间变量采用有限元离散，时间变量采用向后Euler格式离散.数值实验验证了算法的有效性.
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| 关 键 词： | Navier-Stokes方程 有限元方法 两重网格 并行算法 |
| 收稿时间： | 2018-11-07 |
| 修稿时间： | 2019-01-16 |
Parallel Finite Element Algorithms Based on Two-grid Discretization for Time-dependent Navier-Stokes Equations |
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| DING Qi,SHANG Yueqiang. Parallel Finite Element Algorithms Based on Two-grid Discretization for Time-dependent Navier-Stokes Equations[J]. Chinese Journal of Computational Physics, 2020, 37(1): 10-18. DOI: 10.19596/j.cnki.1001-246x.8000 |
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| Authors: | DING Qi SHANG Yueqiang |
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| Affiliation: | School of Mathematics and Statistics, Southwest University, Chongqing 400715, China |
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| Abstract: | Based on two-grid discretization and domain decomposition, three finite element parallel algorithms for unsteady Navier-Stokes equations are proposed. The key idea of the algorithms is to solve nonlinear problem firstly by Oseen iteration method on a coarse grid, and then to solve Oseen, Newton or Stokes problem in parallel on a fine grid to correct the coarse grid solution at each time step, respectively. Conforming finite element pairs are used for spatial discretization and backward Euler scheme for temporal discretization. Numerical results are shown to verify effectiveness of the algorithms. |
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| Keywords: | Navier-Stokes equations finite element method two-grid method parallel algorithm |
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