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

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.