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Non Boussinesq approximation convective flow

Posted by shikhabhuyanshikhabhuyan  
Non Boussinesq approximation convective flow
January 27, 2018 03:49AM
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);

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;
where, th[j] are non-dimentional tempeeratures and Th and Tl and dimensional hot wall and cold wall temperature.
3. New densities are calculated : rhos[j]=(1.0-(beta*(temp[j]-T0)));
4. New velocites are calculated: uxs[j]=uxsum/rhos[j];

However, I am unable to get the correct results.
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