A natural formulation for the solution of two-dimensional or axisymmetric inverse problems

A new method is proposed to solve inverse problems for compressible, non- viscous, rotational flows. Though a time-dependent technique is used to solve the Euler equations, it is based on a fundamentally novel formulation. The time-dependent methods proposed thus far rest on the notion that the initial geometry of a body is guessed and that it satisfies some prescribed design data. As opposed to previous definitions, the grid in the present formulation is defined by flow properties; once a steady solution is reached, the grid is formed by a set of streamlines and lines orthogonal to the streamlines. The Euler equations are then written on the assumption that a set of independent variables coincides with the stream function and with a curvilinear co-ordinate along the lines orthogonal to the streamlines. The present method, based on the lambda-formulation, may be used to solve direct problems as well as inverse problems. (K.K.)