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Kato-Launder modification

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The Kato-Launder modification is an ad-hoc modification of the turbulent production term in the k equation. The main purpose of the modification is to reduce the tendency that two-equation models have to over-predict the turbulent production in regions with large normal strain, i.e. regions with strong acceleration or decelleration.

The transport equation for the turbulent energy, k, used in most two-equation models can be written as:

\frac{\partial}{\partial t} \left( \rho k \right) +
\frac{\partial}{\partial x_j} 
 \rho k u_j - \left( \mu + \frac{\mu_t}{\sigma_k} \right) 
 \frac{\partial k}{\partial x_j}
P - \rho \epsilon - \rho D

Where P is the turbulent production normally given by:

P = \tau_{ij}^{turb} \frac{\partial u_i}{\partial x_j}

Where \tau_{ij}^{turb} is the turbulent shear stress tensor given by the Boussinesq assumption:

Failed to parse (unknown function\defeq): \tau_{ij}^{turb} \defeq - \overline{\rho u''_i u''_j} \approx 2 \mu_t \widetilde{S_{ij}^*} - \frac{2}{3} \rav{\rho} k \delta_{ij}


Kato, M. and Launder, B. E. (1993), "The Modeling of Turbulent Flow Around Stationary and Vibrating Square Cylinders", Proc. 9th Symposium on Turbulent Shear Flows, Kyoto, August 1993, pp. 10.4.1-10.4.6.

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