How to use dynSmagorinsky model correctly ?
Posted July 9, 2014 at 18:47 by rkc.cfd
Tags sgs, turbulence
This is a good reference for why not to use upwind schemes for LES
Quote:
Originally Posted by alberto
I think it is a tradeoff between stability and accuracy. In a finite volume code, your global accuracy is second order anyway. If you use higher order schemes for the convection term you can have some benefit, but you have also to evaluate how important this benefit compared to the standard linear scheme.
I'll try to give you some information of why central schemes are generally preferred in LES and then point you to some reference that is surely more authoritative than me
The order of accuracy gives you information on the dependency of the error on the local size of the discretization (See Ferziger and Peric book). So you might be led to think you simply need to increase the order of the scheme to be safe and do not dissipate too much, to avoid losing information on your turbulence structures due to the dissipation. Unfortunately the story is not so short.
R. Mittal, P. Moin (AIAA Journal, 0001-1452 vol.35 no.8 pp. 1415-1417, 2007, doi: 10.2514/2.253) showed that the numerical dissipation of high-order upwind schemes removes a significant amount of energy from the resolved range of wave numbers, affecting especially the high wavenumbers part, which becomes significantly contaminated by diffusion and dispersion errrors.
This did not happen with energy-conserving central schemes, which do not introduce dissipation (diffusion error).
Why this difference? You find an explanation for example in A. Aprovitola, F. M. Denaro, J. Comp. Phys, 194(1), 329-343 ( http://dx.doi.org/10.1016/j.jcp.2003.09.027 ) , who also describes some upwinded-biased scheme that should be suitable for LES. What the say is essentially that if you discretize the derivatives of your equation with schemes that have non-symmetric stencils you obtain modified wavenumbers with imaginary part that does not tend to disappear. This imaginary part is the responsible of the diffusion error that leads to energy loss.
This problem does not appear in central schemes, which are characterized by real modified wave-numbers. The real part is responsible of the dispersion error, leading to energy pile-up, but the diffusion error is not present.
Best,
I'll try to give you some information of why central schemes are generally preferred in LES and then point you to some reference that is surely more authoritative than me
The order of accuracy gives you information on the dependency of the error on the local size of the discretization (See Ferziger and Peric book). So you might be led to think you simply need to increase the order of the scheme to be safe and do not dissipate too much, to avoid losing information on your turbulence structures due to the dissipation. Unfortunately the story is not so short.
R. Mittal, P. Moin (AIAA Journal, 0001-1452 vol.35 no.8 pp. 1415-1417, 2007, doi: 10.2514/2.253) showed that the numerical dissipation of high-order upwind schemes removes a significant amount of energy from the resolved range of wave numbers, affecting especially the high wavenumbers part, which becomes significantly contaminated by diffusion and dispersion errrors.
This did not happen with energy-conserving central schemes, which do not introduce dissipation (diffusion error).
Why this difference? You find an explanation for example in A. Aprovitola, F. M. Denaro, J. Comp. Phys, 194(1), 329-343 ( http://dx.doi.org/10.1016/j.jcp.2003.09.027 ) , who also describes some upwinded-biased scheme that should be suitable for LES. What the say is essentially that if you discretize the derivatives of your equation with schemes that have non-symmetric stencils you obtain modified wavenumbers with imaginary part that does not tend to disappear. This imaginary part is the responsible of the diffusion error that leads to energy loss.
This problem does not appear in central schemes, which are characterized by real modified wave-numbers. The real part is responsible of the dispersion error, leading to energy pile-up, but the diffusion error is not present.
Best,
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