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]+1/2g[7]+2/3*(g[0]-1.0); // g[1] g[7] g[0] stand for the m=M.f
pyy=1/6g[1]-1/2g[7]+2/3*(g[0]-1.0); // g[0]-1.0 stands for the density fluctuation
pxy=g[8];
qxx=1/3*(g[0]-1.0)+g[3]*g[3]-pxx;
qyy=1/3*(g[0]-1.0)+g[5]*g[5]-pyy;
qxy=1/3*(g[0]-1.0)+g[3]*g[5]-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[7]=s[8]=1/tau;
Is my formula q,pxx,pxy,pyy qxx,qyy,qxy wrong? Who can help me? Thank you so much.
best regards,
bruce