关于定常Navier-Stokes方程非协调有限元三种迭代方法的研究  

Study of three iterative finite element method on the stability of nonconforming Navier-Stokes equations

作　　者：高嘉伟 张翀[2] 李剑 GAO Jia-wei;ZHANG Chong;LI Jian(School of Arts and Sciences,Shaanxi University of Science&Technology,Xi′an 710021,China;School of Geography and Environment,Baoji University of Arts and Sciences,Baoji 721013,China)

机构地区：[1]陕西科技大学文理学院,陕西西安710021 [2]宝鸡文理学院地理与环境学院,陕西宝鸡721013

出　　处：《陕西科技大学学报》2019年第6期170-174,共5页Journal of Shaanxi University of Science & Technology

基　　金：国家自然科学基金项目(11771259);陕西省科技厅自然科学基础研究计划项目(2018JQ4039)

摘　　要：利用低阶非协调有限元配对P 1NC-P 1,通过简单迭代、Oseen迭代和牛顿迭代三种不同的迭代方法求解定常不可压缩流Navier-Stokes方程.从理论的角度讨论了三种迭代方法的稳定性,从数值角度在收敛速度、收敛率和粘性三方面进行比较.结果表明,三种迭代方法具有优化阶的收敛性;在大粘性情况下,牛顿迭代格式收敛速度最快;在小粘性情况下,仅Oseen迭代格式可求解Navier-Stokes问题.Based on the lowest order nonconforming finite element pairing P 1NC-P 1,the Navier-Stokes equations of steady incompressible flow are solved by three different iteration methods:simple-iteration,Oseen-iteration and Newton-iteration.The stability of three iterative methods is discussed theoretically.The convergence speed,convergence rate and viscosity are compared from the perspective of numerical value.Numerical experiments demonstrate that the three iterative methods have the convergence of the optimization order.With large viscosity,Newton-iteration has the fastest convergence speed.When viscosity is small,the Navier-Stokes problem can only be solved through Oseen-iteration scheme.

关 键 词：非协调有限元 简单迭代 Oseen迭代 牛顿迭代 定常NAVIER-STOKES方程 

分 类 号：O241.82[理学—计算数学]