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J. Comp. Math., 29 (2011), pp. 415-440. |
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A New Stabilized Subgrid Eddy Viscosity Method Based on Pressure Projection and Extrapolated Trapezoidal Rule for the Transient Navier-Stokes Equations Minfu Feng 1, Yanhong Bai 2, Yinnian He 3, Yanmei Qin 4 1 School of Mathematics, Sichuan University, Chengdu 610064, China2 Department of Mathematics, Taiyuan Teachers College, Taiyuan 030012, China 3 Faculty of Science, Xian Jiaotong University, Xian 710049, China 4 Key Laboratory of Numberical Simulation of Sichuan Province, Neijiang 641112, China Received 2008-12-13 Accepted 2010-12-22 Available online 2011-6-27 doi:10.4208/jcm.1101-m2996 Abstract We consider a new subgrid eddy viscosity method based on pressure projection and extrapolated trapezoidal rule for the transient Navier-Stokes equations by using lowest equal-order pair of finite elements. The scheme stabilizes convection dominated problems and ameliorates the restrictive inf-sup compatibility stability. It has some attractive features including parameter free for the pressure stabilized term and calculations required for higher order derivatives. Moreover, it requires only the solutions of the linear system arising from an Oseen problem per time step and has second order temporal accuracy. The method achieves optimal accuracy with respect to solution regularity. Key words: Subgrid eddy viscosity model, Pressure AMS subject classifications: 65N30, 76D05. Email: fmf@wtjs.cn, baiyanhong1982@126.com |