Non Boussinesq approximation
 

Hi,
I need to simulate natural convection in square cavity (bottom wall heated) without using Boussinesq approximation. I need to take the density changes into account with non-Boussinesq approximation. Can I solve this with an incompressible solver with treating density as constant? I need help about the formulation and way of solving.

With regards,
Hari

if you are outside the hypothesis of linearity (small variation of temperature) required by Bousinnesq model, you must use the full compressible model

Non Boussinesq approximation
 

Thank you for replying. I need to develop a pressure based solver without boussinesq approximation. Is it possible to work on incompressible flows without treating density as constant.

If the density can vary, then the flow by definition is not incompressible. however, you can develop segregated solvers for variable density flows. One example of such a solver can be found in a JCP paper by Hou and Mahesh. If you put their names into google scholar, the second or third entry will point you to a pdf version of that paper.

Non Boussinesq approximation
 

Thankyou for replying.
I was referring to the following ASME J.heat transfer paper where they say the flow is incompressible with non boussinesq approximation in a differentially heated cavity. I have mentioned the details of the paper below.

A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity
P. Kumar and V. Eswaran
J. Heat Transfer,2010,Volume 132,Issue 2,

Non Boussinesq approximation
 

But doesn't "incompressible" just mean that the density is not a function of pressure? Isn't constant density just an additional simplification? I would think that an (idealized) incompressible fluid could still have the density a function of temperature or concentration. Isn't bouyancy just the result of density differences?

we should define the incompressible by "partial P/partial rho", in natural convecion problem, the density varies, but it is still a incompressible flow.