Stability of an efficient Navier-Stokes solver with Navier boundary condition

Jie Liao; Xiao-Ping Wang

doi:10.3934/dcdsb.2012.17.153

Article Contents

2012, Volume 17, Issue 1: 153-171. Doi: 10.3934/dcdsb.2012.17.153

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Stability of an efficient Navier-Stokes solver with Navier boundary condition

Jie Liao^1, and
Xiao-Ping Wang^2,

1.
School of Science, East China University of Science and Technology, Shanghai, 200237
2.
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received: February 28, 2011

Revised: June 30, 2011

Published: December 2011

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Abstract

In this paper, we study the stability of an efficient numerical scheme based on pressure separation for the Navier-Stokes equations with Navier slip boundary condition in a bounded domain with smooth boundary. The method was introduced in [7, 8] for the Navier-Stokes equation with no-slip boundary condition which decouples the updates of pressure and velocity through explicit time stepping for pressure. The scheme was shown to be very efficient and unconditionally stable. In this paper, we extend this pressure separation method to the problem with Navier slip boundary condition and prove the unconditional stability of the resulting numerical scheme under certain condition on the curvature of the boundary.

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Mathematics Subject Classification: Primary: 65N12, 35Q30; Secondary: 35B35.

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References

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