Reynolds-Stress Model Dual-Time-Stepping Computation of Unsteady Three-Dimensional Flows

An efficient and robust implicit methodology for the integration of the unsteady three-dimensional compressible Favre-Reynolds-averaged Navier-Stokes equations with near-wall Reynolds-stress closure is developed. The five mean-flow and seven turbulence transport equations are discretized on a structured deforming grid, using an O(Δx 3 ) finite volume upwind-biased MUSCL scheme. Time integration uses an implicit O(Δt 2 ) dual-time-stepping procedure with alternating-direction-implict subiterations (with approximate Jacobians designed to minimize the computing time requirements of the implicit phase for the Reynolds stresses, so that the computational overhead of the Reynolds-stress seven-equation closure, compared to a two-equation closure, is less than 30% per iteration), based on a dynamic criterion of subiterative convergence. Grid-deformation velocities associated with solid-wall displacement are computed using a Laplacian operator. The method is validated by comparison with experimental data for 1) two-dimensional pitching oscillations of a NACA-0012 airfoil and 2) three-dimensional shock-wave oscillation in a transonic channel. The influence of the various parameters of the method is analyzed in detail