Improper integrals in the formulation of a supersonic inverse problem

摘要

An inverse design method based on the residual-correction concept has been developed and applied to aerodynamic design of wings for Japanese SST. The method uses an supersonic inverse problem formulated into integral equations. During the process of the formulation, we have encountered mathematical difficulties to deal with improper integrals suffered by singularities. These difficulties have been solved using the extended idea of Hadamard and Cauchy's concepts of integrals. Thus, the mathematical consistency of the inverse problem formulation has been guaranteed. In addition, a satisfactory design result which has been obtained by means of the method is presented.