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Grid Reynolds is above 2 but Central Linear convection scheme works !

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Old   April 21, 2012, 13:00
Question Grid Reynolds is above 2 but Central Linear convection scheme works !
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Dear Foamers,
As you know in linear central scheme of convection term the grid Reynolds (=U*dx/nu) number should be less than 2. If it would be more than 2, the results should be diverged or wrong because of minus in coefficient.

I have simulated a 1*1 m2 lid-driven cavity with the Reynolds number of 10000 (Re=U*1/nu) and 200*200 grids which leads to grid Reynolds in range of 50. it is so far from 2 but results are in good agreement with Ghia (1982) benchmark.
My question:
Why central scheme works in this high grid Reynolds number?
Has it any artificial viscosity been added in OpenFOAM?

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Old   April 23, 2012, 11:32
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Hello, Maysam,

the restriction of Re_cell <= 2 when using the central differencing scheme (CDS) is a sufficient, not a neccessary stability-criterion! (refer to e.g. Ferziger/Peric if you want to know more)

In regions where the solution is more or less smooth (e.g. streamwise direction in channel flow or your lid driven cavity case), the cell reynolds number can be pretty high without any oscillations to appera. It's not neccessary to introduce numerical diffusion to achieve an acceptable stability behavior using CDS.

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