# Kato-Launder modification

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The Kati-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.

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

## References

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.