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Volume 7, Issue 4
Operator Splitting Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions

Y. Li & K. Li

Int. J. Numer. Anal. Mod., 7 (2010), pp. 785-805.

Published online: 2010-07

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  • Abstract

In this paper, the $\theta$ scheme of operator splitting methods is applied to the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind with the Navier-Stokes operator. Firstly, we introduce the multiplier such that the variational inequality is equivalent to the variational identity. Subsequently, we give the $\theta$ scheme to compute the variational identity and consider the finite element approximation of the $\theta$ scheme. The stability and convergence of the $\theta$ scheme are showed. Finally, we give the numerical results.

  • Keywords

Navier-Stokes Equations, Nonlinear Slip Boundary Conditions, Operator Splitting Method, $\theta$-Scheme, Finite Element Approximation.

  • AMS Subject Headings

35Q30, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-785, author = {}, title = {Operator Splitting Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {4}, pages = {785--805}, abstract = {

In this paper, the $\theta$ scheme of operator splitting methods is applied to the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind with the Navier-Stokes operator. Firstly, we introduce the multiplier such that the variational inequality is equivalent to the variational identity. Subsequently, we give the $\theta$ scheme to compute the variational identity and consider the finite element approximation of the $\theta$ scheme. The stability and convergence of the $\theta$ scheme are showed. Finally, we give the numerical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/752.html} }
TY - JOUR T1 - Operator Splitting Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 785 EP - 805 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/752.html KW - Navier-Stokes Equations, Nonlinear Slip Boundary Conditions, Operator Splitting Method, $\theta$-Scheme, Finite Element Approximation. AB -

In this paper, the $\theta$ scheme of operator splitting methods is applied to the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind with the Navier-Stokes operator. Firstly, we introduce the multiplier such that the variational inequality is equivalent to the variational identity. Subsequently, we give the $\theta$ scheme to compute the variational identity and consider the finite element approximation of the $\theta$ scheme. The stability and convergence of the $\theta$ scheme are showed. Finally, we give the numerical results.

Y. Li & K. Li. (1970). Operator Splitting Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions. International Journal of Numerical Analysis and Modeling. 7 (4). 785-805. doi:
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