Implicit implementation of two-equation turbulence models in compressible navier-stokes methods

In the past, numerous CFD studies have reported slow numerical convergence of turbulent flows, particularly in flow regions where production and dissipation are both large. The numerical difficulties include stiffness caused by the presence of an additional time scale, singular behaviour near solid boundaries and the source terms which appear in the model equations. Most researchers implement the turbulence models into Navier-Stokes codes using uncoupled procedures where the model equations and mean flow equations are solved sequentially. A simultaneous solution of all equations (coupled procedure) has not attracted considerable attention. The objectives of the present work are: (a) to develop a new implicit Riemann solver for turbulent flows based on finite volume method and (b) to examine the accuracy and efficiency of well known, as well as, recently developed low-Re two-equation turbulence models in conjunction with the implicit solver.