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Volume 29, Issue 4
A New Stabilized Subgrid Eddy Viscosity Method Based on Pressure Projection and Extrapolated Trapezoidal Rule for the Transient Navier-Stokes Equations

Minfu Feng, Yanhong Bai, Yinnian He & Yanmei Qin

DOI: 10.4208/jcm.1101-m2996

J. Comp. Math., 29 (2011), pp. 415-440.

Published online: 2011-08

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  • 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.

  • Keywords

Subgrid eddy viscosity model, Pressure projection method, Extrapolated trapezoidal rule, The transient Navier-Stokes equations.

  • AMS Subject Headings

65N30, 76D05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-415, author = {Minfu Feng, Yanhong Bai, Yinnian He and Yanmei Qin}, title = {A New Stabilized Subgrid Eddy Viscosity Method Based on Pressure Projection and Extrapolated Trapezoidal Rule for the Transient Navier-Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {4}, pages = {415--440}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1101-m2996}, url = {http://global-sci.org/intro/article_detail/jcm/8485.html} }
TY - JOUR T1 - A New Stabilized Subgrid Eddy Viscosity Method Based on Pressure Projection and Extrapolated Trapezoidal Rule for the Transient Navier-Stokes Equations AU - Minfu Feng, Yanhong Bai, Yinnian He & Yanmei Qin JO - Journal of Computational Mathematics VL - 4 SP - 415 EP - 440 PY - 2011 DA - 2011/08 SN - 29 DO - http://doi.org/10.4208/jcm.1101-m2996 UR - https://global-sci.org/intro/article_detail/jcm/8485.html KW - Subgrid eddy viscosity model, Pressure projection method, Extrapolated trapezoidal rule, The transient Navier-Stokes equations. AB -

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.

Minfu Feng, Yanhong Bai, Yinnian He and Yanmei Qin. (2011). A New Stabilized Subgrid Eddy Viscosity Method Based on Pressure Projection and Extrapolated Trapezoidal Rule for the Transient Navier-Stokes Equations. Journal of Computational Mathematics. 29 (4). 415-440. doi:10.4208/jcm.1101-m2996
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