Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-752
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 4 : pp. 785–805
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Navier-Stokes Equations Nonlinear Slip Boundary Conditions Operator Splitting Method $\theta$-Scheme Finite Element Approximation.