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Time dependent simulation of the Driven Lid Cavity at High Reynolds Number

N. Cardoso, P. Bicudo
CFTP, Departamento de Fisica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
arXiv:0809.3098 [physics.flu-dyn] (18 Sep 2008)

@article{cardoso2008time,

   title={Time dependent simulation of the Driven Lid Cavity at High Reynolds Number},

   author={Cardoso, N. and Bicudo, P.},

   journal={Arxiv preprint arXiv:0809.3098},

   year={2008}

}

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In this work, numerical solutions of the two dimensional time dependent incompressible flow, in a driven cavity at high Reynolds number Re, are presented. At high Re, there is a controversy. Some studies predicted that the flow is steady, others found time dependent non-steady flow, either periodic or aperiodic. In this study, the driven lid cavity is successfully solved using a very fine grid mesh, for Re up to $30 000$. We discretize the Vorticity-Stream formulation of the Navier-Stokes equation with the SSPRK(5,4) scheme in a $1024times1024$ grid. Using this very fine grid, the results obtained converge to a stationary solution. Detailed results for Re between $5 000$ and $30 000$ are presented. The driven lid cavity problem is solved with a NVIDIA GPU using the CUDA programming environment with double precision.
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