# Y+ value for Large Eddy Simulation

Posted August 31, 2020 at 15:35 by MikeBravo

Explanation of Y+ as it relates to viscous sublayer and advection scheme:

Quote:

yes, at least in the viscous sublayer. The size of your grid cell (or the number of points per unit length) determine the smallest scale you can catch on a given grid. From information theory, the Nyquist theorem tells us that we need at least 2 points per wavelength to represent a frequency (we need to be able to detect the sign change). However, 2 points per wavelength is just for Fourier-type approximations. For other schemes like O1 FV you need a lot more, maybe 6 to 10 to accurately capture a wavelength. Let's assume that you have the same grid in all of the flow (i.e. high resolution everywhere, no grid stretching or such). Then the smallest scale you can capture is determined by your grid and scheme, the better/finer, the smaller the scale.

OF course, most grids will coarsen away from the wall, so the smallest scale will "grow bigger" away from the wall as well

Ha, that's the crux of LES of course, the bigger y+, the fewer the small scales you will catch, but does that change the result of the bigger scales?

The answer is not straight forward, but I'll try to make it short:

Let's talk about NS-equations (or any non-linear conservation eqns). The scales represented in the equations are coupled by the non-linearity of the equations, i.e. what happens on one scale will (eventually) reach all other scales (also known as the butterfly effect). So the NS eqns represent the full "nature" with all its scales and interactions. We now truncate our "nature" by resolving only the larger scales, since our grid is too coarse.... what will happen? Will the large scales be influenced by the lack of small scales?

Hell, yeah, they will. We are lacking the balancing interaction of the small scales, since we don't have these scales. We are also lacking the physical effects that take place at small scales (dissipation).... so we have production of turbulence at large scales, the energy is handed down through the medium scales but is NOT dissipated at the small scales, since they are simply not present in our computation. Will that influence the large scales? Definitely!

That's why LES people add some type of viscosity (effect of small scales) to their computations, otherwise, their simulations would very likely just blow up!

hope this help!

cheers

OF course, most grids will coarsen away from the wall, so the smallest scale will "grow bigger" away from the wall as well

Ha, that's the crux of LES of course, the bigger y+, the fewer the small scales you will catch, but does that change the result of the bigger scales?

The answer is not straight forward, but I'll try to make it short:

Let's talk about NS-equations (or any non-linear conservation eqns). The scales represented in the equations are coupled by the non-linearity of the equations, i.e. what happens on one scale will (eventually) reach all other scales (also known as the butterfly effect). So the NS eqns represent the full "nature" with all its scales and interactions. We now truncate our "nature" by resolving only the larger scales, since our grid is too coarse.... what will happen? Will the large scales be influenced by the lack of small scales?

Hell, yeah, they will. We are lacking the balancing interaction of the small scales, since we don't have these scales. We are also lacking the physical effects that take place at small scales (dissipation).... so we have production of turbulence at large scales, the energy is handed down through the medium scales but is NOT dissipated at the small scales, since they are simply not present in our computation. Will that influence the large scales? Definitely!

That's why LES people add some type of viscosity (effect of small scales) to their computations, otherwise, their simulations would very likely just blow up!

hope this help!

cheers

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