[hityangsir]

Hi All,

For the LES simulation, there are two categories of simulation:
wall resolved LES, which resolved the Bounday layer,
wall modeled LES, which modeled the Boundary layer using algebraic or RANS,

It is easy to understand the wall-modeled LES, the models will presents the shear stress accordingly
but for wall resolved LES, it should be more close to the original LES meaning, which using only grid size to filter small scale of vortices.

So what is the criteria to using wall modeled LES rather than wall resolved LES?
, why modeled boundary layer is so important (feasible in the near future?)?

and what is the grid size density should be for wall resolved LES?

And for non-uniform grid, the shortest or the longest should be characteristic length of filtering?

Thank you for your kind reply

Best regards

[FMDenaro]

wall-resolved grids in LES is quite similar to DNS grid...you do not filter at such scales

[hityangsir]

Dear Professor Denaro,

Thank you very much for your kind replying.
So basically, there is no grid size criteria to distinguish Wall-resolved LES and DNS? Is there any mathematical foundation of what the mesh density should be?
Recently, I read some papers about wall resolved LES and wall modeled LES, there are several different suggestions I have read.
For every cubic computational box with side length equal to the boundary layer thickness (delta)
nx = 10 ny = 25 nz = 10 (Chapman 1979)
nxnynz = 1,000 (Piomelli et al. 1989)
nxnynz = 4096 (Schumann 1979)
nx = 5~32 ny = 16~32 nz = 15-32 (Choi 2011)
Also some people use x+, y+, z+ to measure.

However, for the wall resolved LES, there seems no much reported, some paper grid size seems to be at the same level for WMLES only.
dx+ = 100 dz+ = 20 ny = 10 (Chapman 1979,Poimelli2002)
dx+=50~130 dz+ = 15~30 ny = 10~30(Choi&Moin 2011)

[FMDenaro]

a general advice for wall-resolved LES is to have 3-4 computational nodes whithin y+<1 (viscous sublayer).

cell sizes in non-confined directions can be also up h+ =O(20)-O(30)

[hityangsir]

Originally Posted by FMDenaro

a general advice for wall-resolved LES is to have 3-4 computational nodes whithin y+<1 (viscous sublayer).

cell sizes in non-confined directions can be also up h+ =O(20)-O(30)

Thank you for your advice for Wall-resolved LES.
Is there any mathematical explanation or physical foundation for the grid density?

And for the wall modeled LES, how do you think the large differences of the grid density from different researchers?

[FMDenaro]

the better explanation is that the grid size in the boundary layer should be enough fine to ensure locally Re_h = O(1). This way, convective and diffusive fluxes are resolved at the same magnitude scale.

[hityangsir]

Thank you Filippo,
Sorry I don't really get it.
Isn't it that the viscous and inviscid fluxes are evaluated by the flux splitting and discretinization schemes like MUSCL?

[FMDenaro]

Originally Posted by hityangsir

Thank you Filippo,
Sorry I don't really get it.
Isn't it that the viscous and inviscid fluxes are evaluated by the flux splitting and discretinization schemes like MUSCL?

I used the cell Reynolds number, if it is computed with the reference lenght based on your local mesh size and the result is O(1) that means you are allowing diffusive and convective flux to be computed at same accuracy on that scale. The y+ lenght is nothing else a local Re number.

This is a general observation, without considering the type of scheme you are using

[hityangsir]

locally "Re_h = O(1)" means that grid size can as fine as Kolmogrov scale? is that right?

[FMDenaro]

yes, obviously near walls you do not have a single characteristic scale