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12.7.2 Reynolds Stress Transport Equations

The exact transport equations for the transport of the Reynolds stresses, $\rho \overline{u'_i u'_j}$, may be written as follows:

\underbrace{\frac{\partial}{\partial t} ( \rho \; \overline{u... ...t)} \right]}_ {\mbox{$D_{T,ij} \equiv$ Turbulent Diffusion}}

 \; \; + \underbrace{\frac{\partial}{\partial x_{k}} \left[
... ...'_{i} \theta})}_{\mbox{$G_{ij} \equiv$ Buoyancy Production}}

+ \underbrace{\overline{ p \left ( \frac{\partial u'_{i}}{\p... ...}}{\partial x_k}}}_{\mbox{$\epsilon_{ij} \equiv$ Dissipation}}

 \underbrace{- 2 \rho \Omega_k \left( \overline{u'_j u'_m} ... ...\underbrace{S_{\rm user}}_{\mbox{User-Defined Source Term}} (12.7-1)

Of the various terms in these exact equations, $C_{ij}$, $D_{L,ij}$, $P_{ij}$, and $F_{ij}$ do not require any modeling. However, $D_{T,ij}$, $G_{ij}$, $\phi_{ij}$, and $\epsilon_{ij}$ need to be modeled to close the equations. The following sections describe the modeling assumptions required to close the equation set.

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© Fluent Inc. 2006-09-20