where t is time, Pk is the turbulent kinetic energy generated by the average velocity gradient, Pb is the turbulence
kinetic energy generated due to buoyancy, and YM is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate such that Pb = 0 and YM = 0. Sk and Sε are source terms that can be defined by the user, and k and ε are turbulent Prandtl numbers. The model constants for the realizable
k–ε turbulence model are ε = 1.2, C1 ε = 1.44, C2ε = 1.92, k = 1.0, and C3ε = tanh(up/u v), where up and u v are the velocity components parallel and normal to gravity, respectively.