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Test Cases for Numerical Methods in Two Dimensional Transonic Flows

At the Specialists' Meeting on transonic aerodynamics:l held by AGABD in Paris during
September 1968, a number of papers were presented describing developments currently in progress on
numerical methods for calculating inviscid transonic flows round aerofoil sections in two dimensions.
Even though most of these methods use the full equations of motion without simplification, there are
a number of fadtors - the discretisation of the partial differential equations, the numerical '
techniques used to solve them, and the approximations to the boundary conditions on the aerofoil and
at infinity - which will all tend to introduce errors of unknown magnitude which it is difficult to
estimate purely from internal considerations.
At discussions held during the meeting, and confirmed by the subsequent Technical Evaluation
Report 2, it was suggested that a set of test cases should be issued by AGARD in order to provide
checks of the accuracy of the various methods preposed.
In considering the choice of these test cases, it is clearly essential that accurate theoretical
results should be available for the chosen shapes; experimental results are usually unsatisfactory
because of the presence of viscous effects and of wind tmnel constraints. It is also desirable
that examples should be included of both lifting and non-lifting aerofoils, with and without camber,
and in subcritical and supercritical flow. For this purpose it is considered that only two existing
methods can provide the requisite accuracy.
In this method solutions are calculated for both the aerofoil shapes and pressure
distribution, neither of which can be specified in advance; but by varying a number
of basic parameters a large variety of shapes can be obtained which are of practical
interest, and both subcritical and supercritical (shockefree) flows can be considered.
The method in its latest. form is capable of designing lifting (cambered) aerofoils,
and although most of the examples suggested below are symmetrical profiles at zero
incidence, one lifting supercritical case has also been included.