natural convection

hello everyone
i’am trying to simulate natural convection in square cavity with thermal lattice boltzmann model. the situation is a cavity with isothermal vertical walls and adiabatic horizantals walls. in right T=Th and in the left T=Tc. the velocity u=0 and v=0 in all the boundary. can you pleeeeeeeeeeeeease help me to right the equations of boundary condition for the flow(about f) and for tempreture (about g) f and g are distributions functions.
think you

see Mohammad book
Lattice Boltzman Method
by A.A Mohammad
good luck

Hello everyone,

I am trying to write a FORTRAN code to simulate natural convection in heated cavity exactly like ‘Saida 29’. this problem is also mentioned in A.A Mohammad book and is a well-known Bench mark in CFD(I found many paper related to this topic). My code works for Ra=10 ^4, but it does not work for Ra=10^6 and 10^5 and I know this method has this capacity to work even with higher Ra number like 10^8. I tried to follow the A.A Mohammad instruction and also other papers; however, I have not solve this issue. does anyone have a FORTRAN or C++ code which works for RA=10^6 or more?
In advance, Thanks for your consideration

Dear saida and hooman
you can solve your problems by reading this ebook"fundamental and engineering applications with computer codes by A.A.Mohamad"
good luck!