Abstract

The present work gives a brief review of the integral equation method in transonic aerodynamics, with particular emphasis on the works of Nϕrstrud, Nixon and Niyogi. The use of integral equation method can result in significant reduction in computer time, roughly by a factor of 60, compared to the finite difference relaxation procedure. In shock-free symmetrical super-critical flows, the simple solution of Niyogi which delivers results with less than 5 % overall error, may be conveniently used for analysis as well as for design purposes. The direct iteration scheme, applicable to shock-free flow, as well as to flows with shocks, emerges as particularly attractive due to its favourable convergence behaviour and computational simplicity. It is expected to be even more effective for three-dimensional problems. Further, the simple model suggested by Oswatitsch for thin symmetrical profile flow is sufficiently accurate for most practical purposes. For results of high accuracy, a hybrid direct iteration/finite difference procedure is suggested, which would use the converged direct iteration solution of the simple Oswatitsch model as the starting solution for the finite difference procedure.

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