# MRT-LBE-LES D2Q9 smagorinsky model

Hi everyone,
How are you?
I wanna simulate the 2D cavity flow with MRT-LBE at high Reynolds number. But i have a problem with the smagorinsky model according the paper Large eddy simulations with a multiple-relaxation-time LBE model by Manfred Krafczyk and Jonas tolke, Li-Shi Luo.
My results agree with others paper at Re<=7500. But the relative velocity error are keeping e-2 at Re>=10000, that is, the code can’t converge.
The smagorinsky model formula is:
pxx=1/6g+1/2g+2/3*(g-1.0); // g g g stand for the m=M.f
pyy=1/6g-1/2g+2/3*(g-1.0); // g-1.0 stands for the density fluctuation
pxy=g;

``````qxx=1/3*(g-1.0)+g*g-pxx;
qyy=1/3*(g-1.0)+g*g-pyy;
qxy=1/3*(g-1.0)+g*g-pxy;

q=sqrt(2*(qxx*qxx+qyy*qyy+2*qxy*qxy));  // q=sqrt(Q_ij.Q_ij) in the paper, but q=sqrt(2*Q_ij.Q_ij) in the others paper.
tau_0=3*U_bc*MX/Re+0.5;
tau_t=0.5*sqrt(tau_0*tau_0+18*(c*delta)*(c*delta)*q)-0.5*tau_0;
tau=tau_0+tau_t;
s=s=1/tau;
``````

Is my formula q,pxx,pxy,pyy qxx,qyy,qxy wrong? Who can help me? Thank you so much.

best regards,
bruce