Non Boussinesq approximation convective flow

Lattice Boltzmann Method LBM: Algorithms
#1

Dear all,

I have been trying to write a LBM code for convective flow inside a square cavity with non-Boussinesq approximation but it seems certain problem with the algorithm. If anyone can help me out with this…

Algorithm followed:

  1. Macroscopic variables at time step “t” are solved by usual LBE with collision and propagation procedure. The force term is included in the collision step: F=((3w_f[k]RiprprReRe*(rhos[i][j])-rhost)ey[k])/(16eps);

  2. With the available temperature at every lattice nodes, the dimentional temperatures at those lattice points are obtained:
    temp[i][j]= (th[i][j]*(Th-Tl))+Tl;
    where, th[i][j] are non-dimentional tempeeratures and Th and Tl and dimensional hot wall and cold wall temperature.

  3. New densities are calculated : rhos[i][j]=(1.0-(beta*(temp[i][j]-T0)));

  4. New velocites are calculated: uxs[i][j]=uxsum/rhos[i][j];
    uys[i][j]=uysum/rhos[i][j];

However, I am unable to get the correct results.