Boussinesq model for natural convection simulation
To model natural convection and the buoyancy effect in fluid dynamics, it is possible to use the Boussinesq approximation as long as the temperature gradient in the fluid domain is not large.
The figure below shows heated air in a semi cylindrical container. This CFD simulation is transient in nature and it does not require the Boussinesq approximation to simulate buoyancy but nevertheless it has been used in this case.
The Boussinesq approximation is formulated as follow:
Where alpha is the thermal coefficient of expansion
Delta T is the temperature difference between 2 cells.
For more information about the Boussinesq approximation and its applications, check this link out