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Volume 31, Issue 2
A Second Order Modified Characteristics Variational Multiscale Finite Element Method for Time-Dependent Navier-Stokes Problems

Zhiyong Si, Jian Su & Yinnian He

DOI: 10.4208/jcm.1210-m3799

J. Comp. Math., 31 (2013), pp. 154-174.

Published online: 2013-04

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  • Abstract

In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier-Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with $Re$=5000, 7500 and 10000. We present the numerical results as the time is sufficiently long, so that the steady state numerical solutions can be obtained.

  • Keywords

Modified method of characteristics, Defect-correction finite element method, Navier-Stokes problems, Characteristics-based method, Lid-driven problem.

  • AMS Subject Headings

76D05, 76M10, 65M60, 65M12.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-31-154, author = {Zhiyong Si, Jian Su and Yinnian He}, title = {A Second Order Modified Characteristics Variational Multiscale Finite Element Method for Time-Dependent Navier-Stokes Problems}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {2}, pages = {154--174}, abstract = {

In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier-Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with $Re$=5000, 7500 and 10000. We present the numerical results as the time is sufficiently long, so that the steady state numerical solutions can be obtained.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1210-m3799}, url = {http://global-sci.org/intro/article_detail/jcm/9727.html} }
TY - JOUR T1 - A Second Order Modified Characteristics Variational Multiscale Finite Element Method for Time-Dependent Navier-Stokes Problems AU - Zhiyong Si, Jian Su & Yinnian He JO - Journal of Computational Mathematics VL - 2 SP - 154 EP - 174 PY - 2013 DA - 2013/04 SN - 31 DO - http://doi.org/10.4208/jcm.1210-m3799 UR - https://global-sci.org/intro/article_detail/jcm/9727.html KW - Modified method of characteristics, Defect-correction finite element method, Navier-Stokes problems, Characteristics-based method, Lid-driven problem. AB -

In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier-Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with $Re$=5000, 7500 and 10000. We present the numerical results as the time is sufficiently long, so that the steady state numerical solutions can be obtained.

Zhiyong Si, Jian Su and Yinnian He. (2013). A Second Order Modified Characteristics Variational Multiscale Finite Element Method for Time-Dependent Navier-Stokes Problems. Journal of Computational Mathematics. 31 (2). 154-174. doi:10.4208/jcm.1210-m3799
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