I want to simulate a simple non-isothermal flow. My Idea is to compute the fluid flow with LB and the advection-diffusion equation for the temperature with the finite volume method. I would also like to take into account of buoyancy with the Boussinesq approximation.
Do you think is that possible? Can anybody explain me how LB is affected by Boussinesq approximation?

Hi,
I think that indeed it is a very good idea to try to couple OpenLB with a finite volume advection diffusion code (we’ve never done that ). For more informations about the Boussinesq force coupling with LB you can have a look at this paper Guo et al..

I have written quite a bit of finite volume code. If you have the flow field (u,v) from LB and the basic thermal properties of the fluid, it is easy to integrate the thermal solver. Let me know if you want to see some sample code.

I’ve a question for Orestis about the paper by Guo.

I did the Chapman-Enskog expansion but I’m in trouble. I can’t derive the equation (22) on that paper. In particular, i think that the term multiplied by delta_t/2 should be D[sup]2[/sup][sub]1i[/sub]Tsup[/sup], otherwhise I can’t get the equation (23) and so on…