[selig5576]

For the K-Epsilon, model I am unsure how to appropriately discretize the production term (image attached). I am currently trying 2nd-order central differencing of the terms to retain second order accuracy, however I know that it will run into issues for high Reynolds numbers. I was curious if this was sufficient given I don't yet want to do any type of WENO or ENO.

EDIT: To clarify and give substance to this topic.

1. What I am curious about is if central differencing of the production term is sufficient.

2. Something I am confused about is how in Griebel's book he performs some type of mixed finite differencing on the 2D production term (eqn 10.31 and its U velocity counter part), which I don't understand given there is no mixed derivatives.

[selig5576]

Any suggestions or thoughts?

[FMDenaro]

I have no personal experience about this modelling, however my general opinion is that you should consider using the same spatial operators you used for the other terms. In general, that depends also on the use of either FD or FV methods. In the latter, you have to consider the volume integral of the production term.
For the time integration you have to consider that a production term can become stiff and cause problems in the numerical stability.

[Hamidzoka]

I have a prior experience in FV with other turbulence models.
The integral form of the production term at cell boundaries needs to approximate velocity derivatives and a central scheme will be a proper choice for that.