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=((3*w_f[k]*Ri*pr*pr*Re*Re*(rhos

*[j])-rhost)*ey[k])/(16*eps);
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2. With the available temperature at every lattice nodes, the dimentional temperatures at those lattice points are obtained:

temp*[j]= (th**[j]*(Th-Tl))+Tl;
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where, th*[j] are non-dimentional tempeeratures and Th and Tl and dimensional hot wall and cold wall temperature.
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3. New densities are calculated : rhos*[j]=(1.0-(beta*(temp**[j]-T0)));
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4. New velocites are calculated: uxs*[j]=uxsum/rhos**[j];
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uys*[j]=uysum/rhos**[j];
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However, I am unable to get the correct results.