Favre averaged Navier-Stokes equations
From CFD-Wiki
Instantaneuos Equations
The instantaneous continuity equation (1), momentum equation (2) and energy equation (3) 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:
| (4) |
Where the trace-less viscous strain-rate is defined by:
| (5) |
The heat-flux, , is given by Fourier's law:
| (6) |
Where the laminar Prandtl number is defined by:
| (7) |
To close these equations it is also necessary to specify an equation of state. Assuming a calorically perfect gas the following relations are valid:
| (8) |
Where , , and are constant.
The total energy is defined by:
| (9) |
Insert Reference |
Equations (1)-(9), supplemented with gas data for , , and perhaps , form a closed set of partial differential equations, and need only be complemented with boundary conditions.
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