# Favre averaged Navier-Stokes equations

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(Difference between revisions)

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\frac{\partial \rho}{\partial t} + | \frac{\partial \rho}{\partial t} + | ||

\frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0 | \frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0 | ||

- | </math> (1) | + | </math> (1) |

:<math> | :<math> |

## Revision as of 08:09, 5 September 2005

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.