CALCULATION OF TRANSONIC-FLOWS BY A FIELD INTEGRAL-EQUATION METHOD

A field integral equation method is developed to solve the two-dimensional compressible potential equation for transonic flow over airfoils with embedded shocks at subsonic freestream Mach numbers. The perturbation velocities are induced by linear internal source and vorticity distributions on the mean camber line of the airfoil and nonlinear field source distributions external to the airfoil surface. Derivatives are calculated in the computational plane, and those in the physical plane are determined by using the Jacobian of the transformation. An O-type grid is applied to reduce the numerical errors in the region close to the location where the shock wave occurs. The calculations have been carried out for NACA 0012, parabolic arc, and circular arc airfoils at various subcritical freestream Mach numbers. The results of the present method are compared with earlier results and are shown to be in good agreement.