二维稳态Navier-Stokes方程的有限元方法  

Finite Element Method for Two-Dimensional Steady Navier-Stokes Equation

作　　者：郝家雄 张羽 陶霞[1] HAO Jiaxiong;ZHANG Yu;TAO Xia(School of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006,China)

机构地区：[1]湖南理工学院数学学院,湖南岳阳414006

出　　处：《湖南理工学院学报（自然科学版）》2023年第1期17-20,共4页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：国家自然科学基金青年科学基金项目(12001189);湖南省普通高等学校教学改革研究项目(湘教通[2021]298号,HNJG-2021-0772);湖南理工学院学位与研究生教学改革研究项目(YJG2021A002)。

摘　　要：Navier-Stokes方程是流体力学中一类重要的数学物理方程,其相关控制方程是非线性的.设计二维Navier-Stokes方程的有限元格式,并实现该算法.对于非线性项采用Newton迭代格式.数值结果表明,该方法不仅具有稳定性,而且具有较好的收敛性.Navier-stokes equation is an important kind of mathematical and physical equations in fluid mechanics,and the relevant control equation is nonlinear.In this paper,the finite element scheme was constructed for the Navier-stokes equation,and this algorithm was realized.Newton iterative scheme was used for the nonlinear term.The numerical results show that the finite element method is not only stable,but also has good convergence property.

关 键 词：NAVIER-STOKES方程 有限元方法 NEWTON迭代 收敛 

分 类 号：O242.21[理学—计算数学]