1. Introduction#

We place ourselves in the framework of linear acoustics, in a limited environment, which considers a compressible fluid, experiencing small amplitudes of disturbances or fluctuations in pressure and density.

The equations to be solved are those describing the local balance of the fluid and the conservation of mass, accompanied by the viscoacoustic linear behavior relationship (of the hysteretic type).

A modeling option was developed in Code_Aster, making it possible to study stationary linear acoustic propagation at low frequency, in a bounded environment, for propagation domains with a complex topology, i.e. solving the Helmholtz equation under the conditions mentioned.

To know the paths of propagation of energy in the fluid, the acoustician has the active acoustic intensity \(I\):

(1.1)#\[ I=\ frac {1} {2}\ text {Re}\ left [p {v} ^ {\ text {*}}}\ right]\]

And reactive acoustic intensity \(J\):

(1.2)#\[ J=\ frac {1} {2}\ text {Im}\ left [p {v} ^ {\ text {*}}}\ right]\]

Where \({v}^{\text{*}}\) refers to the complex conjugate of vibratory speed. Knowledge of these quantities provides additional information that is very important in solving problems of all kinds, for example the measurement of powers radiated by machines, the recognition and location of sources.