A FINITE ELEMENT STRATEGY TO COMPUTE AERODYNAMIC SOUND WITH LIGHTHILL'S ANALOGY

The prediction of aerodynamic sound generated by low-Mach-number flows typically involves solving a multi-scale problem in which the radiated acoustic energy is only a very small fraction of the energy contained in the aerodynamic fluctuations. While this scale separation justifies the use of acoustic analogies, in a numerical implementation the results can be very sensitive to the definition of the sources, because the radiated sound becomes the result of delicate cancellations of aerodynamic sources of opposite sign. In this work, a finite element strategy is proposed to compute turbulence noise based on Lighthill's equation, in which the second derivatives of the quadrupole source term are transferred to the shape functions by defining each quadrupole as a compact group of monopoles each defined through a Dirac delta function. This implementation forces the numerical errors in the source representation to behave as spurious quadrupole sources instead of lower order multipole sources, which are more efficient at low frequencies and can pollute the entire acoustic solution.