Locally Linearized Solution of Lifting Transonic Flow by Method of Parametric Differentiation - Harijono Djojodihardjo (Journal of Mathematical and Fundamental Sciences, 1971)
The governing equation of transonic small disturbance flow present a non-linear partial differential equation which is difficult to solve. The method of parametric differentiation reduces the non-linear partial differential equation of transonic flow into an ordinary differential equation with variable coefficient, which is generally much simple to solve. Further simplification is introduced, as also done in the method of local linearization, by assuming (1-M12) to vary sufficiently slowly, so that in some part of the analysis its derivatives with respect to x can be disregarded. Based upon these methods, the lifting transonic flow was analyzed. For the subsonic and supersonic parts, closed form solutions were obtained. For the case M1 â‰ˆ 1, the method yields an integral equation, which can be solved by an iterative scheme starting from the non-lifting solution.