带阻尼项定常Navier-Stokes方程的并行两水平有限元算法  

Parallel Finite Element Algorithms Based on Two-grid Discretizations for the Steady Navier-Stokes Equations with Damping Term

作　　者：王国梁 郑波 尚月强 WANG Guoliang;ZHENG Bo;SHANG Yueqiang(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《计算物理》2023年第5期535-547,共13页Chinese Journal of Computational Physics

基　　金：重庆市自然科学基金(cstc2021jcyj-msxmX1044);西南大学科研创新项目(SWUS23057)资助。

摘　　要：基于两重网格离散和区域分解技术,提出数值求解带阻尼项定常Navier-Stokes方程的三种并行两水平有限元算法。其基本思想是首先在粗网格上求解完全的非线性问题,以获得粗网格解,然后在重叠的局部细网格子区域上并行求解Stokes、Oseen和Newton线性化的残差问题,最后在非重叠的局部细网格子区域上校正近似解。数值算例验证了算法的有效性。Based on two-grid discretizations and domain decomposition techniques,this paper presents three parallel finite element algorithms for numerically solving the steady Navier-Stokes equations with damping term.The basic idea of the present algorithms is to first solve a fully nonlinear problem on a coarse grid to get a coarse grid solution,then solve Stokes,Oseen,and Newton linearized residual problems in parallel in overlapping local fine grid subdomains,and finally update the approximate solution in non-overlapping fine grid subdomains.The effectiveness of the proposed algorithms is demonstrated by some numerical examples.

关 键 词：阻尼项 NAVIER-STOKES方程 两水平方法 有限元方法 并行算法 

分 类 号：O241.82[理学—计算数学]