As mentioned in the last section, noise sources for the Lighthill equation can arise from several sources. These include displacement of the fluid by a moving boundary, pressure fluctuations on surfaces within the CFD calculation (these may or may not be wall boundary conditions), as well as interior flow features. The first of these sources is called a monopole source. The second is called a dipole source, if the surface is stationary, or it is called a rotating dipole source, if the surface is rotating at a fixed angular velocity about an axis. Finally, interior sources are usually referred to as quadrupole sources.

A generalized version of the Lighthill equation that represents the three possible noise sources was first presented by Williams and Hawkins [180] as follows:

(15–5)

where is the Dirac delta function describing the moving surface geometry ( is non-zero in the fluid region and zero at the moving boundary), is the normal velocity of the surface, and is the fluid stress tensor given by:

(15–6)

The first term on the right hand side of Equation 15–5 represents the monopole source. The second term represent the dipole sources (possibly rotating). The third term represents the quadrupole sources.