Rayleigh-Bènard convection

Hi, im new to LB methods and was looking for some pointers.

Im assigned to do the following.

rhodu = ??P + rho v*?^2u ? rhoalpha*gT

dT = k*?^2*T

‘’ Use the Lattice Boltzmann model for miscible fluids to solve the equations
above for the case where the fluid is confined by two horizontal plates
separated by a distance d, and where u = 0, that is, no-slip boundary conditions.
The system is heated from below so that T = 1 at the bottom plate and T = 0 at
the top plate. Use a lattice size 128x64. Initially, take T = 0 everywhere.
Sensible parameter values are alpha*g =0.0005, v = 0.25 and k = 0.025. ‘’

I have to use a hexagonal (D2Q7) lattice.

What would I need to do step by step to solve this system numerically?

If anyone have some code I might build upon that would be much appreciated. (c++/java)

Thanks in advance

This is certainly an interesting homework assignment.

Here are two documents which will help you to get it done.

The article on thermal fluids by Guo e.a.

The tutorial on unit conversions in LB, which contains a section on thermal fluids.