On coupling the Reynolds-averaged Navier-Stokes equations with two-equation turbulence model equations

Two methods for coupling the Reynolds-averaged Navier-Stokes equations with the q-ω turbulence model equations on structured grid systems have been studied; namely a loosely coupled method and a strongly coupled method. The loosely coupled method first solves the Navier-Stokes equations with the turbulent viscosity fixed. In a subsequent step, the turbulence model equations are solved with all flow quantities fixed. On the other hand, the strongly coupled method solves the Reynolds-averaged Navier-Stokes equations and the turbulence model equations simultaneously. In this paper, numerical stabilities of both methods in conjunction with the approximated factorization-alternative direction implicit method are analysed. The effect of the turbulent kinetic energy terms in the governing equations on the convergence characteristics is also studied. The performance of the two methods is compared for several two- and three-dimensional problems.