引用本文:刘青, 尚月强.非定常Navier-Stokes方程有限元算子分裂算法[J].西南大学学报(自然科学版),2019,41(3):75~83
【打印本页】   【HTML】   【下载PDF全文】   查看/发表评论  【EndNote】   【RefMan】   【BibTex】
←前一篇|后一篇→ 过刊浏览    高级检索
本文已被:浏览 183次   下载 167 本文二维码信息
码上扫一扫!
分享到: 微信 更多
非定常Navier-Stokes方程有限元算子分裂算法
刘青, 尚月强
西南大学 数学与统计学院, 重庆 400715
摘要:
在连续解的正则性假设条件下,基于亚格子稳定模型和算子分裂方法提出了非定常不可压Navier-Stokes方程的有限元算子分裂算法.其主要思想是:利用算子分裂方法把非线性项和不可压缩项分开,首先求解一个线性化的Burger's问题得到有限元解uhn+1/2,然后再求解一个Stokes问题得到解uhn+1.证明了速度的误差估计关于时间是一阶收敛的,并给出数值实验验证了理论的正确性.
关键词:  不可压缩流体  Navier-Stokes方程  有限元  算子分裂方法  误差估计
DOI:10.13718/j.cnki.xdzk.2019.03.011
分类号:O241.82
基金项目:重庆市基础科学与前沿技术研究专项项目(cstc2016jcyjA0348).
The Finite Element Operator Splitting Method for the Incompressible Navier-Stokes Equations
LIU Qing, SHANG Yue-qiang
School of Mathematics and Statistic, Southwest University, Chongqing 400715, China
Abstract:
Under the regularity assumptions on the continuous solution, we provide a finite element operator splitting method for the simulation of unsteady incompressible Navier-Stokes equations, which is based on the subgrid model. It is a two-step scheme in which the nonlinearity and incompressibility are split into different steps. First, a linear Burger's system is solved, and the solution of the finite element uhn+1/2 is obtained. Then a Stokes problem is solved, and its solution uhn+1 is obtained. We derive the error bound of the approximate velocity which is first-order in time. Numerical experiments have verified the correctness of the theoretical analysis.
Key words:  incompressible flow  Navier-Stokes equation  finite element  operator splitting method  error analysis
手机扫一扫看