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Transient Error Estimate with icoErrorEstimate ?

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Old   June 25, 2009, 13:54
Default Transient Error Estimate with icoErrorEstimate ?
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Christophe Kassiotis
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Hello everybody

I would like to estimate the errors in a transient computation (for instance flow around a cylinder bluff body) with low Reynolds number (around 200). So the idea was to use an error estimate like icoErrorEstimate.

I launch some computations and I observe that the error is at it biggest behind the bluff body,for few points in the Van Karman vortex street. With a rather coarse mesh, the error estimate give something around 1.8 in relative value (mag(e)/mag(U)) for some of this points. Elsewhere, the error is rather small (less than 10%) - but the flow is quasi static elsewhere.

My guess was that the transient term is not estimate corectly with icoErrorEstimate, but maybe i'm wrong.
Indeed, the equation solved is:

errorEstimate<vector> ee( resError::div(phi, U) - resError::laplacian(nu, U) == -fvc::grad(p) );

According to the PhD of H. Jasak, p 196-200, one should take care of the transient term, adding something like (Eq 4.117)

\frac{\rho\Phi-\rho\Phi^0}{\Delta t} to this equation

So do I need to add this term ? Is this normal that nothing like this appears in icoErrorEstimate ? Maybe I didn't get something...

Other questions : if I want a global error estimate of the computation error, should I consider the max/mean total/relative error ? Is it possible to get an error approximate for the pressure field ?

Thank you in advance.


CK
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Old   June 28, 2009, 05:24
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Hrvoje Jasak
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Formally, you need to separate the temporal error from its spatial counterpart.

For the spatial error, consider the ddt as a fixed source term and use the residual estimate as before.

For the temporal component, you need some form of Richardson extrapolation, depending on how much reliable temporal data you have got.

Please note: you are NOT allowed to sum up the two errors for the "total error"

Enjoy,

Hrv
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