Boundary Elements in Primitive Variables and FWH Revisited – Viscosity Effect

A boundary element formulation for aeroacoustics in primitivevariables is presented. For the Euler equations, the formulationis addressed in details. The result is a self-contained set ofboundary integral equations, coupling velocity and pressure. Forthe sake of simplicity, only the formulation for bodies in uniformtranslation, such as airplanes is presented. This allows one toobtain some further elaboration of the equations with respect ofexisting results. This in turn yields a deeper understanding ofthe formulation. The final result may be considered as anextension of the Kirchhoff, and Ffowcs Williams and Hawkingsformulations, in that the expression for the pressure is fullyequivalent those, but an expression for the velocity is alsoavailable. The most interesting result however is that, havingstarted from a primitive variable formulation, the finalexpression may be considered also as an extension of thequasi-potential formulation to vortical flows (indeed, the twoformulations coincide if the non-linear terms are neglected).