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…
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);
With the available temperature at every lattice nodes, the dimentional temperatures at those lattice points are obtained:
where, th[i][j] are non-dimentional tempeeratures and Th and Tl and dimensional hot wall and cold wall temperature.
New densities are calculated : rhos[i][j]=(1.0-(beta*(temp[i][j]-T0)));
New velocites are calculated: uxs[i][j]=uxsum/rhos[i][j];
However, I am unable to get the correct results.