Hi,

I am new to LES with some background in solving RANS using upwind methods. Is it possible to use flux-splitting/TVD schemes in LES discretisation. My limited understanding is that LES solving the Navier-stokes equation using some form of subgrid? filtering model instead of turbulence models.

Shuo

"My limited understanding is that LES solving the Navier-stokes equation using some form of subgrid"

In LES, the Navier Stokes eqs are solved in the grid (the mesh that you are using). In the subgrid scales (i.e. scales smaller than your mesh at a considered point) the turbulence is modelized by some empirical equations (see Smagorinski for example).

" filtering model instead of turbulence models" There is turbulence models, because the subgrid scales are modelized. But it's not the same models as in RANS. In LES the models are only for subgrid scales, i.e. effects that your mesh cannot see because it's too coarse.

Hope it helps

But you still need to discretise the equations right?

But you still need to discretise the equations right?

Yes sure, you discretize by FVM or FEM... there is additional "subgrid scale" viscosity terms appearing in N-S.

Hi,

You can use TVD scheme for LES. However LES subgrid models result mostly in a very low level of added turbulent viscosity (typically of the same order of magnitude or slightly higher than the physical viscosity). Consequently the use of a TVD scheme with a high level of built-in dissipation can hide the effects of subgrid model.

Two global classes of approach are in use to alleviate this drawback: - Use a standard TVD scheme without explicit subgrid modeling, hopping that the numerical dissipation is able mimic the subgrid dissipation. It works rather fine for flows with complex geometry at high Reynolds number.

-Use an explicit subgrid model with high-order upwind schemes, hybrid centered-upwind schemes or centered scheme with specific smoothing filtering. The Ducros sensor can be used for the shock-capturing part of the scheme to discriminate between regions of gradient due to turbulence (where the shock capturing dissipation is set to 0) and regions of gradient due to pressure waves.

There is a third possibility: design a scheme with a built-in dissipation as close as possible as a subgrid one by using the same approach as the dispersion-optimized schemes : for a given stencil, reduce the formal order of accuracy and use the saved degree of freedom to improve the subgrid model-likeness.

Hope this helps,

Lionel scheme that yield a numerical dissipation