LES sfs flux

[bronise777]

Martín, M. Pino, U. Piomelli, and G. V. Candler. "Subgrid-Scale Models for Compressible Large-Eddy Simulations." Theoretical and Computational Fluid Dynamics 13, no. 5 (2000): 361–76. https://link.springer.com/article/10.1007/PL00020896
This is the energy equation



But in the pc_smagorinsky_sfs_term function,
flx(iv, UEDEN) = -sigmadx * Uface[0] - sigmady * Uface[1] - sigmadz * Uface[2];
flx(iv, UEDEN) = flx(iv, UEDEN) - cp * Cs2 / PrT * flux_T;
I have two problems, following the above formula sigmadx * Uface[0] sign seems to be positive and should have a coefficient of 1/2.

[marchdf]

hmmmm I would agree on the missing 1/2. And it seems like there is a sign issue. Is it on the Qj term or the Jj term? I am swamped with some things right now but if you have an argument for one or the other, I would be happy to look into it in a couple of days.

[bronise777]

The sign issue seems like on the Jj. But in my test, Jj is very small. So this bug only has a little influence.

[baperry2]

I believe the term is correct as is, although there are certainly a lot of different possible sign conventions that could be leading to confusion.

First, the stress term for LES should resemble the viscous stress term, and it does. See: Combustion/PeleC/blob/203736c2009bc114b6aecdfdf40ef46eeb4859f8/Source/Diffterm.H#L447. Notably, the sign of the force term and the sign of the energy flux due to that force should be the same.

I believe the factor of two is an omission from the Martin et al paper. Equation 37 refers to Knight et al 1998, specifically Equation 19, which indicates that the factor of 1/2 is accounted for when introducing the model for $J_j$. (note they have also adopted the opposite sign convention for $\tau_{ij})$

[bronise777]

I'm sorry, there are no sign errors here, But the sigmadx * Uface[0] seems to be only the first half of the following formula.

[baperry2]

The sigma term in that equation comes from molecular viscosity. In PeleC, the molecular and LES/turbulent terms are computed separately. The molecular component is computed in pc_diffusion_flux in Diffterm.H