Computational treatment of source terms in two-equation turbulence models

The source terms in turbulence models require careful treatment to obtain a stable discretization. The choice between implicit and explicit treatment has to be made. This can be done either on the basis of individual terms or on the basis of the exact Jacobian of the source terms. A comparison of both methods shows that the latter is generally applicable and superior to the first, approximate method with respect to convergence speed. This comes from the possibility of using the multigrid technique with the exact method, whereas this is not always possible with the approximate method. It is also shown that, in principle, for robustness a time-step restriction for the source terms has to be introduced to prevent the turbulence quantities from becoming negative or infinitely large. An approximation of the appropriate time step is calculated. Practical results, however, indicate that the time-step restriction is not always necessary. Different two-equation turbulence models are investigated confirming the generality of the approach.