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Tony July 30, 2001 18:29

Exact 2D NS solution for benchmarking?
Hi there,

I need an exact 2D incompressible NS solution (analytical) for benchmarking.

I know that there is a 3D solution by Ethier and Steinman in Int J Num Meth Fluids. But I could not find this journal in our library.

Thanks for any help.


John C. Chien July 30, 2001 18:43

Re: Exact 2D NS solution for benchmarking?
(1). "Exact solutions of the Navier-Stokes equations",Chapter V, in Schlichting's book of "Boundary Layer Theory". (1960 edition. there are newer editions)

NAME July 30, 2001 19:30

Re: Exact 2D NS solution for benchmarking?
I'm not too sure if this link will work for you but here is the link to the journal homepage. I'm sure you can order a copy from here if you want.

Prof Ethier is at the University of Toronto. Maybe he has a postscript copy on his web page.

Two good books which have the analytical solutions to the NS equations are:

Incompressible Flow. R.L.Panton Fundamental Mechanics of Fluids. I. Currie

zhaoli guo July 31, 2001 09:34

Re: Exact 2D NS solution for benchmarking?

I am also testing a new CFD method, and I constructed some analytical solutions of the NS equation, please contact with me


kalyan July 31, 2001 14:50

Re: Exact 2D NS solution for benchmarking?
This paper has an exact solution for a decaying 2-D TG vortex. You can test your solver in the two extreme limits (high Re and Stokes limit) by varying the Re. I find it useful to quantify the artificial dissipation relative to physical dissipation at various grid spacings.

A Non-staggered Grid, Fractional Step Method for Time-Dependent Incompressible Navier-Stokes Equations in Curvilinear Coordinates Yan Zang, Robert L. Street, Jeffrey R. Koseff

Journal of Computational Physics, Vol. 114, No. 1, September 1, 1994

If you need more complicated solutions of NS equations, look for solutions based on Lie Groups. I can not remember a reference off hand, but you search using NS equations and Lie groups and I am sure you can find something on the net or in your library.

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