Wave paths in transient polytropic flow

An accurate method of locating wave paths in transient polytropic flows is introduced and is justified both physically and analytically. The method, w hich is exact in steady flows, is useful in its own right and also as a ben chmark for assessing the accuracy of simpler methods that are easier to use . In the absence of strong unsteadiness, simple methods are shown to be suf ficiently accurate for practical purposes even with relatively coarse grid sizes. Very simple methods are sufficient in the case of low Mach numbers. More complex methods, all iterative, are shown to be necessary at higher Ma ch numbers. When flows contain regions of rapidly varied flow, either spati al or temporal, inaccurate predictions are shown to be inevitable. This is because the average speed of wave propagation (V+/-c) between two points in (x, t) space cannot be expressed as a function of conditions at these poin ts alone. When such regions exist, high accuracy is achievable only with sm all grid sizes. (C) 2000 Elsevier Science Ltd. All rights reserved.