Large eddy simulation grid requirement mention about Delta X+ = 100, Delta Z+ = 30 and y+ = 1. Y+ is known but what do you mean by Delta x+ and Delta Z+, x is streamwise and z is spanwise directions,
they are the computational step sizes normalized in wall units.
For example, generally, it is well known that the step dx (dimensional) is made dimensionless by a characteristic lenght L so that the non dimensional step is dx*=dx/L.
In turbulence, it is assumed a non-dimensional step that resembles the cell Reynolds number. In confined flows (channel or pipe) the u_tau velocity is used (tau_wall= rho*u_tau^2) and the Re_tau is defined as u_tau*delta/ni where delta=L is for example the half height of a channel.
dx*=dx/delta = (u_tau*ni)*dx/(u_tau*ni)*delta =ni/(u_tau*delta) *(u_tau*dx/ni)
therefore:
dx+ =u_tau*dx/ni = Re_tau* dx*
they are the computational step sizes normalized in wall units.
For example, generally, it is well known that the step dx (dimensional) is made dimensionless by a characteristic lenght L so that the non dimensional step is dx*=dx/L.
In turbulence, it is assumed a non-dimensional step that resembles the cell Reynolds number. In confined flows (channel or pipe) the u_tau velocity is used (tau_wall= rho*u_tau^2) and the Re_tau is defined as u_tau*delta/ni where delta=L is for example the half height of a channel.
dx*=dx/delta = (u_tau*ni)*dx/(u_tau*ni)*delta =ni/(u_tau*delta) *(u_tau*dx/ni)
therefore:
dx+ =u_tau*dx/ni = Re_tau* dx*
In the book "Turbulent Flows" by S.B. Pope (2001), the author explains non-dimensional wall units in physical terms instead of computational. The Reynolds stress at the wall must be zero, so the stress at the wall must be purely viscous (i.e. frictional). One can define a length scale for the purely viscous stress at the wall called the viscous length scale, defined as
d_v = nu*(rho/tau_w)^(1/2) = nu/u_tau, viscous length scale [m],
nu = kinematic viscosity (molecular), [m^2/s],
rho = fluid density, [kg/m^3],
tau_w = wall stress, [N/m^2],
u_tau = (tau_w/rho)^(1/2) friction velocity, [m/s],
A friction Reynolds number can be defined as
Re_tau = u_tau*d/nu, dimensionless,
d = a distance, [m],
such that if the distance is the viscous length scale d=d_v, Re_tau = 1. Non-dimensional "wall units" are x+ = x/d_v, y+=y/d_v, z+=z/d_v, so if you estimate the viscous lengthscale d_v then you can estimate normalized grid dimensions for your simulation.
The spanwise and streamwise resolution needed for turbulent boundary layer LES depends on your choice of wall model / your choice of SGS model. For incompressible LES, I recommend taking a look at the chapter on LES wall models in the book "LES for incompressible flows" by P. Saguat (2006). The author does a thorough review of the contemporary state of the art for LES wall models, and the author notes that part of the problem for LES of turbulent boundary layers is that turbulent kinetic energy is produced in the "buffer layer" just outside of the viscous sub layer in a turbulent boundary layer (Re_tau = order(1-10)). Therefore you either have to have a very fine resolution LES, like the y+=1 requirement that you stated, and/or use a wall model.
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