非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法  

A NON-CONFORMING FINITE ELEMENT METHOD OF SUBGRID VISCOSITY METHOD FOR THE NON-STATIONARY LINEARIZED NAVIER-STOKES EQUATIONS

作　　者：孔花[1] 冯民富[2] 覃燕梅[1] 

机构地区：[1]内江师范学院,数学与信息科学学院/四川省高等学校数值仿真重点实验室,四川内江641112 [2]四川大学数学学院,成都610064

出　　处：《计算数学》2013年第1期99-112,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(编号:11271273);四川省教育厅青年基金项目(编号:11ZB175)资助

摘　　要：本文结合子格粘性法的思想,空间采用非协调Crouzeix-Raviart元逼近,时间采用Crank-Nicolson差分离散,对非定常线性化Navier-Stokes方程建立了全离散的子格粘性非协调有限元格式.对稳定性和误差估计作出了详细的分析,得出了最优的误差估计.最后,通过数值算例进一步验证了该方法的稳定性和收敛性.For the non-stationary linearized Navier-Stokes equations, a non-conforming finite el- ement method of subgrid viscosity method is presented, where Crouzeix-Raviart noncon- forming finite element is employed, and the Crank-Nicholson scheme is used for time dis- cretization. Stability and convergence of the method is proved. The error estimation results show that the method achieves optimal accuracy with respect to solution regularity. The numerical results were given, which demonstrate the stability and convergence of the method presented.

关 键 词：非定常线性化Navier—Stokes方程 子格粘性方法 Crouzeix—Raviart元 

分 类 号：O241.82[理学—计算数学]