JOURNAL OF SOUND AND VIBRATION www.elsevier.com/locate/jsvi Journal of Sound and Vibration 261 (2003) 583–612 An advanced time approach for acoustic analogy predictions D. Casalino* Laboratoire de M! ecanique des Fluides et Acoustique, Ecole Centrale de Lyon, Avenue Guy de Collongue, 69131 Ecully Cedex, France Received 10 December 2001; accepted 1 May 2002 Abstract This paper deals with a new interpretation of the retarded time approach that is widely used in the prediction of acoustic fields from moving sources. A hierarchical inversion between the emission time and the reception time leads to advanced time approach. This consists in projecting the current status of a source in the observer time domain where the received signal is progressively built. The practical relevance of this methodology lies on two statements: no retarded time equations must be solved; an aerodynamic noise prediction can be processed parallelly to the aerodynamic computation. Theoretically, the advanced time approach differs from the retarded time approach only in one aspect. A signal emitted at a given instant by a point source, moving at subsonic as well as supersonic velocity, is received only one time by an observer moving at subsonic velocity. Consequently, only one value of the advanced time corresponds to a value of the emission time. The advanced time approach is herein applied to a retarded time solution of the Ffowcs Williams and Hawkings equation proposed by Farassat. The noise radiated by elementary acoustic sources in complex motion is then computed and checked against analytical solutions. r 2002 Elsevier Science Ltd. All rights reserved. 1. Introduction Two strategies can be adopted for the prediction of acoustic fields, one based on the Computational AeroAcoustic approach (CAA), the other based on integral formulations. CAA methods consist in solving the flow governing equations including acoustic fluctuations by means of classical CFD methods (finite difference, finite volume, finite elements, etc.) with high-accuracy (low dispersion) numerical schemes. Therefore, reasonable cost solutions are restricted to *Tel.: +33-472-18-65-39; fax: +33-472-18-91-43. E-mail address: damiano.casalino@ec-lyon.fr (D. Casalino). 0022-460X/03/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII:S0022-460X(02)00986-0