Are you wanting to drive the flow by virtue of a temperature gradient resulting in changes in density, which ultimately influence pressure? You see, there is a problem in all CFD approaches. The continuity equation is based on density, which may or may not be directly related to pressure and/or temperature. The momentum equations (Navier-Stokes) include pressure , as these arise from Newton's 2nd Law. There is no immediate equation for pressure, yet we must solve these together. We must make some sort of substitution or transformation of variables (for example P=rho*R*T for an ideal gas) so as to bring pressure into the governing differential equations where we can solve it. There are several ways of doing this. It depends on what software you're using. No model is perfect for every case. FLUENT may work best for one class of problems, while OpenFOAM may work better for another class of problems, while PHOENICS may work better for yet another class of problems. It's not practical (or affordable) for you to buy every commercial CFD code and run your problem on each. You need to be specific about what you want to do and what fluid interactions you hope to capture and then you need to look for an approach (for example FEM, FDM, FVM, lattice-Boltzmann, or whatever) can deliver the right result for your particular problem.

Thank you very much for your answer Mr Benton, I ve understood your explanation.