A review is presented of theoretical methods in aerodynamics and aeroacoustics which lead to the present approach. A formulation is developed for the analysis of three-dimensional, unsteady, and viscous flows. The integral solution to the Ffowcs Williams and Hawkings equation mixes surface and volume contributions. The surface terms are treated following the traditional boundary element technique. Special care is taken in revealing the hidden singularities of curved surfaces. The volume terms are treated following a cell-based approach. The concept of finite-part of singular integrals is used to interpret these terms. A computational procedure is proposed to determine simultaneously the pressure and velocity fields around bodies moving in incompressible and compressible fluids. Finally, current and future directions of research regarding the present method are pointed out and discussed.

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