Unconditional stable solutions of the Euler equations for two-and three-d wings in arbitrary motion

The work presented here shows the unsteady inviscid results obtained for the two-and three-dimensional wings which are in rigid and flexible oscillations. The results are generated by a finite volume Euler method. It is based on the Runge-Kutta time stepping scheme developed by Jameson et al.. To increase the time step which is limited by the stability of Runge-Kutta scheme, the implicit residual smoothing which is modified by using variable coefficients to prevent the loss of flow physics for the unsteady flows is engaged in the calculations. With this unconditional stable solver the unsteady flows about the wings in arbitrary motion can be received efficiently. The two- and three-dimensional rectangular wings which are in rigid and flexible pitching oscillations in the transonic flow are investigated here, some of the computational results are compared with the experimental data. The influence of the reduced frequency for the two kinds of the wings are researched. All the results given in this work are reasonable.