Effects of numerical method of source terms in turbulence models

Eddy viscosity models have been widely used in many engineering applications of turbulence. Usually there are additional source terms on the right side of the turbulent governing equations, which may play an important role in the computation of Navier-Stokes equations. Stiffness that results from source terms is analyzed in details and the significant balance between production term and destruction term is discussed, together with point implicit approach, an universal way to solve equations with source terms. Afterwards both S-A turbulence model with weak stiffness and k-ω SST turbulence model with strong one are taken as examples to show the specific treatments concerning about the different source terms between these two. The paper ends with numerical tests of RAE 2822 airfoil transonic flow, which demonstrates that the methods above can overcome the stiffness from the source terms and improve the stability of the computation effectively.