Favre averaged Navier-Stokes equations
From CFD-Wiki
The instantaneous continuity equation, momentum equation and energy equation for a compressible fluid can be written as:
- (1)
- (2)
- (3)
For a Newtonian fluid, assuming Stokes Law for mono-atomic gases, the viscous stress is given by:
Where the trace-less viscous strain-rate is defined by:
The heat-flux, , is given by Fourier's law:
Where the laminar Prandtl number is defined by:
To close these equations it is also necessary to specify an equation of state. Assuming a calorically perfect gas the following relations are valid:
Where and are constant.
The total energy is defined by:
Note that the corresponding expression~\ref{eq:fav_total_energy} for Favre averaged turbulent flows contains an extra term related to the turbulent energy.