Coordinate perturbation and multiple scale in gasdynamics.

Abstract

A simple way of applying the coordinate perturbation technique is developed which bypasses the usual transformations of the equations to perturbed coordinates, and which provides the appropriate coordinate stretching by simple algebraic manipulations on the nonuniformly valid expansion obtained by a straightforward expansion from the original equations. Interesting results are obtained by applying the procedure to two gasdynamical problems. In the first, the flowfield around a supersonic two-dimensional wing is determined up to third order, including a uniformly valid representation of the front shock shape. The second concerns the oscillations in a closed tube following an arbitrary initial disturbance, both when the two ends are closed, and when one of the two ends contains an oscillating piston.