[Memet1c]

Hi all,

I would like to know if the following formulation is correct.
I am trying to express the NSEs in conservative form using the incompressible ideal gas model as the buoyancy term.

Incompressible ideal gas assumes:



Where the density only varies with temperature and not pressure.

The NSEs expressed in conservative form:

- Continuity
- Momentum
- Energy

Note that the viscous dissipation and pressure work terms have been omitted from the energy equation.

My question from here is, how do I proceed to solve this system of equations numerically?

Given that I have expressed the density as a function of purely temperature, do I substitute it into my continuity, momentum, and energy equations? Or do I solve my system of equations separately from my equation of state, only updating the density field after marching forward in time.

Any literature recommendations explaining the incompressible ideal gas model in detail, and especially its numerical implementation would be greatly appreciated.