基于H(div)型有限元的非定常Navier-Stokes方程的涡旋黏性法  

H(div) element-based eddy viscosity method for time-dependent Navier-Stokes equation

作　　者：樊新玉 李辉[2] 冯民富[1] FAN Xin-Yu;LI Hui;FENG Min-Fu(College of Mathmatics, Sichuan Univerity, Chengdu 610064, China;Sichuan Petroleum and Gas Construction Engineering Co. Ltd. , Chengdu 610200, China)

机构地区：[1]四川大学数学学院,成都610064 [2]四川石油天然气建设工程有限责任公司,成都610200

出　　处：《四川大学学报（自然科学版）》2017年第6期1159-1168,共10页Journal of Sichuan University(Natural Science Edition)

摘　　要：本文结合涡旋黏性思想与H(div)型有限元(如RT元和BDM元)逼近,对不可压非定常Navier-Stokes方程提出了一种新的稳定化有限元格式.这种格式不但满足守恒条件,而且克服了对流占优引起的振荡.通过半离散有限元格式,本文得到了与约化雷诺数相关而与雷诺数无关的误差估计.A new stabilized finite element formulation for incompressible time-dependent Navier-Stokes equation with high Reynolds number is presented. This formulation combines subgrid eddy viscosity methods with H（div） finite element （for example,RT and BDM finite element） approximation, satisfies the conservation condition, and controls spurious oscillations in the velocities. The stability and error estimate for finite element semidiscrete scheme are derived. The constants in these error estimates are independent of the Reynolds number as well as rely on a reduced Reynolds number.

关 键 词：非定常不可压Navier-Stokes方程 子格涡旋黏性法 高雷诺数 H(div)稳定元 

分 类 号：O242.21[理学—计算数学]