Implementation of k-ω turbulence models in an implicit multigrid method

Three k-omega turbulence models using linear and nonlinear eddy-viscosity formulations are implemented in an implicit multigrid method. Detailed techniques of implementation are presented and discussed. Freezing and limiting strategies are applied to improve robustness and convergence of the muitigrid method. The Wilcox k-omega, k-omega shear-stress transport, and Wilcox-Durbin+ (WD+) models are first tested for flat-plate How, and the results are in good agreement with the empirical correlations. Numerical results for unseparated and separated transonic flows show that the WD+ model using weakly nonlinear eddy viscosity is in better overall agreement with the experimental data. Particularly for the separated flows, the present multigrid diagonalized alternating-direction implicit method provides good convergence without any robustness problems.