Aerodynamic inverse design method for low mach number airfoils

Because of the large disparity between the acoustic wave speed and the waves convected at fluid speed, the accuracy of the solution to the flow fields of non-compressible low Mach number flows is poor and the convergence rate is bad when using the standard convective scheme based on compressible flows. Generally the preconditioning techniques are used to deal with this problem. In the optimization method based on control theory, the Jacobian matrix of adjoint equations and the mxatri of flow equations are similar, so the same difficulties such as oversized numerical viscosity and numerical rigidity exist when solving the adjoint equations. In this paper, a Roe scheme with preconditioning is first deduced. Then a full speed numerical scheme is developed for adjoint equations. Finally, two typical tests about an airfoil and a cascade are presented. The results indicate that the preconditioned adjoint equation method can develop a low Mach number aerodynamic inverse design efficiently.