Extension of Boussinesq turbulence constitutive relation for bridging methods

Bridging methods for turbulence simulation are adaptive eddy-viscosity schemes based on the accuracy-on-demand paradigm, much like hybrid approaches. The object is to resolve more scales of motion than Reynolds-averaged Navier-Stokes (RANS) by suitably reducing the eddy viscosity as a function of grid spacing. Currently, there are two proposals for extending the RANS two-equation model with Boussinesq constitutive relation to bridging methods. In the first approach, it is suggested that the coefficient in the Boussinesq relation be reduced and the transport equations for the length and velocity scales left unaltered for achieving the desired level of viscosity reduction. The second approach suggests that the viscosity reduction is better achieved by suitably modifying the transport equations rather than altering the Boussinesq coefficient. In this paper, we compare the merits of the two methods in two important benchmark cases: flows past circular cylinder and backward facing step. Three types of evaluations are performed. First, we verify the requisite viscosity reduction is indeed achieved in the calculations. Then, we compare some crucial qualitative aspects of the solutions from the two methods. Finally, we evaluate the two solutions against experimental data for the same level of intended viscosity reduction.