Volume 5, Issue 1
Gauge-Uzawa Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions

Hailong Qiu, Liquan Mei & Zhangxin Chen

DOI:

Int. J. Numer. Anal. Mod. B, 5 (2014), pp. 46-56

Published online: 2014-05

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  • Abstract

In this paper, the Gauge-Uzawa method is applied to solve the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is a variational inequality of the second kind with the Navier-Stokes operator. In [1], a multiplier was introduced such that the variational inequality is equivalent to the variational identity. We give the Gauge-Uzawa scheme to compute this variational identity and provide a finite element approximation for the Gauge-Uzawa scheme. The stability of the Gauge-Uzawa scheme is showed. Finally, numerical experiments are given, which confirm the theoretical analysis and demonstrate the efficiency of the new method.

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@Article{IJNAMB-5-46, author = {Hailong Qiu, Liquan Mei and Zhangxin Chen}, title = {Gauge-Uzawa Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2014}, volume = {5}, number = {1}, pages = {46--56}, abstract = {In this paper, the Gauge-Uzawa method is applied to solve the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is a variational inequality of the second kind with the Navier-Stokes operator. In [1], a multiplier was introduced such that the variational inequality is equivalent to the variational identity. We give the Gauge-Uzawa scheme to compute this variational identity and provide a finite element approximation for the Gauge-Uzawa scheme. The stability of the Gauge-Uzawa scheme is showed. Finally, numerical experiments are given, which confirm the theoretical analysis and demonstrate the efficiency of the new method.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/218.html} }
TY - JOUR T1 - Gauge-Uzawa Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions AU - Hailong Qiu, Liquan Mei & Zhangxin Chen JO - International Journal of Numerical Analysis Modeling Series B VL - 1 SP - 46 EP - 56 PY - 2014 DA - 2014/05 SN - 5 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/218.html KW - AB - In this paper, the Gauge-Uzawa method is applied to solve the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is a variational inequality of the second kind with the Navier-Stokes operator. In [1], a multiplier was introduced such that the variational inequality is equivalent to the variational identity. We give the Gauge-Uzawa scheme to compute this variational identity and provide a finite element approximation for the Gauge-Uzawa scheme. The stability of the Gauge-Uzawa scheme is showed. Finally, numerical experiments are given, which confirm the theoretical analysis and demonstrate the efficiency of the new method.
Hailong Qiu, Liquan Mei & Zhangxin Chen. (1970). Gauge-Uzawa Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions. International Journal of Numerical Analysis Modeling Series B. 5 (1). 46-56. doi:
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