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Numerical solution of conservation equations arising in linear wave theory: application to aeroacoustics

Published online by Cambridge University Press:  12 April 2006

SÉBastien M. Candel
SÉBastien M. Candel
Affiliation:
Office National d'Etudes et de Recherches AÉrospatiales (ONERA), and UniversitÉ de Technologie de Compiègne, 92320 Chatillon, France
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Abstract

The propagation of waves in slightly inhomogeneous dispersive media is conveniently described by a geometrical or kinematic theory. In such frameworks the solution of the propagation problem is constructed by (a) deriving a dispersion relation and determining its characteristic lines and (b) solving an equation expressing the conservation of a field invariant like the wave action. This paper is concerned with the implementation of the last step under general field and boundary conditions. The method presented is based on the derivation of a variational system of differential equations for the geodesic elements of the wave front. The elementary cross-section of the wave front is obtained by integration and the principle of conservation of the field invariant directly yields the field amplitude. In addition, suitable jump conditions are derived for treating specular reflexions at solid boundaries. The method is illustrated by specific problems of interest in aeroacoustics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 3 , 5 December 1977 , pp. 465 - 493
Copyright
© 1977 Cambridge University Press

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