The Navier-Stokes equations are solved with the second-order LU-SGS-τTS implicit time-stepping method. The sixth-order symmetric TVD scheme with fifth-order WENO interpolation based on Roe is applied to the convection terms. A boundary layer flow around a flat plate, a low speed flow around the Aerospatial A-profile at high incidence and a transonic flow with shock/boundary interaction around RAE2822 airfoil are computed by Baldwin-Lomax and Spalart-Allmaras models with the transition criterion, respectively. The results show that the approaches capture the transition automatically.

A fully implicit Lower-Upper-Symmetric-Gauss-Seidel (LU-SGS) with pseudo time sub-iteration and the modified Jameson's central scheme are applied to solve thin layer Navier-Stokes(N-S) equations with laminar hypothesis and Baldwin-Lomax(B-L) model for the vortical flows around delta wings at high angles of attack (AOA).To validate the codes,a 65 degree swept delta wing is computed in transonic cases,where M_∞=0.85,α=10°,20° and Re=5×10⁶.Then asymmetrical vortex breakdown flows with M_∞=0.3,and Re=1.3×10⁶,at high AOA around an 80° swept delta wing are presented and discussed.The computational results are compared with experimental data available and good agreement is achieved.

Four turbulence models:algebraic Baldwin-Lomax model with Degani-Schiff modification, two versions of Johnson-King model (J-K90A and J-K92) and two-equation k-g model, are described and evaluated for missile supersonic flow, NASA TN D-712 standard model and the civil airplane wing-body configuration (two-block C-O mesh) transonic flows. The 3-D compressible Reynolds averaged Navier-Stokes (RANS) equations are integrated numerically by central-difference with artificial viscosity scheme, finite volume formulation and explicit multi-step Runge-Kutta algorithm. The turbulence equations of k-g model are explicitly solved in the same way as the RANS. Results show that all models can perform well for attached and mildly separated flows. For large angle-of-attack separated flow over the missile, k-g and J-K92 models match the experimental results much better than those with B-L and J-K90A models. According to the B-L model with some modification, the shock location logs behind those with the other three models for the civil airplane geometry. Model k-g, because of its advantages such as without using normal-to-wall distance, simple source terms and straightforward boundary conditions, performs best in the four models for complex configuration with multi-block mesh system or multi-wall interference. B-L and J-K models, despite of cheapness and robustness, both base on empirical Prandtl mixing-length hypothesis and need to calculate the distance normal to the wall, undoubtedly limiting the application scope of these models for multi-block mesh system and complex geometry.

Grid generation and flow analysis methods for multi-element airfoil based on multi-block point-to-point patched grid technology are developed. Some strategies are developed to improve the efficiency, accuracy and applicability of the method.Several flow cases about multi-element airfoils are computed with the present method in order to validate it. Numerical results are in agreement with experiment data. Flow field visualization shows that the present method has good resolution in flow details.