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Volume 38, Issue 3
A New Stabilized Finite Element Method for Solving Transient Navier-Stokes Equations with High Reynolds Number

Chunmei Xie & Minfu Feng

DOI: 10.4208/jcm.1810-m2018-0096

J. Comp. Math., 38 (2020), pp. 395-416.

Published online: 2020-03

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  • Abstract

In this paper, we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure. We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme. The scheme is proven to possess the absolute stability and the optimal error estimates. Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods, Petro-Galerkin finite element method and streamline diffusion method.

  • Keywords

Transient Navier-Stokes problems, High Reynolds number, The projection of the velocity and pressure, Taylor-Hood elements, The equal order elements.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fmf@scu.edu.cn (Minfu Feng)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-395, author = {Xie , Chunmei and Feng , Minfu}, title = {A New Stabilized Finite Element Method for Solving Transient Navier-Stokes Equations with High Reynolds Number}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {3}, pages = {395--416}, abstract = {

In this paper, we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure. We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme. The scheme is proven to possess the absolute stability and the optimal error estimates. Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods, Petro-Galerkin finite element method and streamline diffusion method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1810-m2018-0096}, url = {http://global-sci.org/intro/article_detail/jcm/15792.html} }
TY - JOUR T1 - A New Stabilized Finite Element Method for Solving Transient Navier-Stokes Equations with High Reynolds Number AU - Xie , Chunmei AU - Feng , Minfu JO - Journal of Computational Mathematics VL - 3 SP - 395 EP - 416 PY - 2020 DA - 2020/03 SN - 38 DO - http://doi.org/10.4208/jcm.1810-m2018-0096 UR - https://global-sci.org/intro/article_detail/jcm/15792.html KW - Transient Navier-Stokes problems, High Reynolds number, The projection of the velocity and pressure, Taylor-Hood elements, The equal order elements. AB -

In this paper, we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure. We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme. The scheme is proven to possess the absolute stability and the optimal error estimates. Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods, Petro-Galerkin finite element method and streamline diffusion method.

Xie , Chunmei and Feng , Minfu. (2020). A New Stabilized Finite Element Method for Solving Transient Navier-Stokes Equations with High Reynolds Number. Journal of Computational Mathematics. 38 (3). 395-416. doi:10.4208/jcm.1810-m2018-0096
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