Analysis and finite element approximation of a Ladyzhenskaya model for viscous flow in streamfunction form
作者:
Highlights:
•
摘要
In this paper we consider a model for the motion of incompressible viscous flows proposed by Ladyzhenskaya. The Ladyzhenskaya model is written in terms of the velocity and pressure while the studied model is written in terms of the streamfunction only. We derived the streamfunction equation of the Ladyzhenskaya model and present a weak formulation and show that this formulation is equivalent to the velocity–pressure formulation. We also present some existence and uniqueness results for the model. Finite element approximation procedures are presented. The discrete problem is proposed to be well posed and stable. Some error estimates are derived. We consider the 2D driven cavity flow problem and provide graphs which illustrate differences between the approximation procedure presented here and the approximation for the streamfunction form of the Navier–Stokes equations. Streamfunction contours are also displayed showing the main features of the flow.
论文关键词:65N30,76M10,78M10,76D03,35Q35,Finite element method,Ladyzhenskaya model,Streamfunction formulation
论文评审过程:Received 16 November 2005, Revised 12 July 2006, Available online 22 September 2006.
论文官网地址:https://doi.org/10.1016/j.cam.2006.07.028