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.




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The Boussinesq approximation is formulated as follow:

boussinesq-approximation

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

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