An LU-SGS(Lower-Upper Symmetric Gauss-Seidel) scheme and improvement for three-dimensional unstructured grid Euler computation are presented.Grid reordering for efficient implementation of the improved LU-SGS and the original LU-SGS is proposed.In order to test the feasibility and efficiency of the improved LU-SGS algorithm,two numerical examples of transonic inviscid flow around an ONERA M6 wing and an LANN supercritical wing are presented.It shows that the numerical results agree well with the experimental data.Moreover,the efficiency of the improved LU-SGS scheme is two times higher than that of the original LU-SGS scheme and seven times higher than that of the explicit Four-Stage-Runge-Kutta scheme.

Based on a distributed parallel computing system,a new approach to the transonic flutter of a flexible wing is presented by coupling the computational fluid dynamics (CFD) method with the computational structural dynamics(CSD)method. by using a transfinite interpolation(TFI) scheme to generate a multi-block C-H moving grid,the aerodynamic analysis is carried out by solving the three-dimensional unsteady Navier-Stokes equations. By coupling with the flutter motion equations,the response of the time history of generalized coordinates is found.The critical velocity is got on the base of the response. by considerally decreasing the computing time,a multidisciplinary analysis code runs on a distributed parallel computer system by using the PVM library.Computational results are presented for the transonic flutter of wings with deformed shapes as found in flutter simulations.

An analysis method of the airfoil flutter system with nonlinear structure at transonic speeds is presented. The unsteady aerodynamic forces are calculated by Navier-Stokes equations. The time histories of structure responses of airfoil are solved by coupling the Navier-Stokes equations and flutter equations. The systems with gap stiffness, cubic type stiffness and cubic structure damping are investigated. The calculated results show that the influence of the structure nonlinearity on flutter speed is sensitive. Due to both the structure and aerodynamic nonlinearity in the flutter system, the oscillation characterstics become very complex.

The 2-D time-dependent compressible Navier-Stokes equations are adopted as the governing equations. The unsteady lift coefficients of airfoil are calculated by Navier-Stokes equations with the implicit LU-NND algorithm, Baldwin-Lomax turbulent model and C-type grids. The fluctuating values of lift coefficient are increased with the enlargement of incidence and Mach number. The buffet onset boundary is defined as the beginning point where the fluctuating values of aerodynamic coefficients are increased suddenly. The fluctuating values of aerodynamic coefficients expresses the buffet strength. The buffet characteristics of supercritical airfoil DFVLR-R2 and airfoil NACA0012 are investigated. The calculating results show that:in the design Mach number range of supercritical airfoil, there are larger buffet onset incidence and less buffet loads. When Mach number is larger than the design Mach number, the buffet onset incidence of supercritical airfoil decreases quickly and there are rather large buffet loads. In the convention airfoil NACA 0012, there are much less buffet onset incidence, larger buffet loads and separated range.

A dual-time scheme is used to solve the unsteady compressible Navier-Stokes equations to obtain the needed airload.The model structural equations of motions are computed simultaneously using the Runge-Kutta method to calculate the aeroelastic static deformations and responses of wings in the time-domain.The O-H type grid around the deforming wings is generated using the improved transfinite interpolation method so that grid generation in each time-step is not too time-consuming.The numerical results show the transonic flutter speed drop and nonlinear characteristics.