Acoustic velocity formulation for Kirchhoff data surfaces

This paper deals with the derivation of an analytical time-domain formulation for the prediction of the acoustic velocity field generated by moving bodies in a medium at rest, according to the Kirchhoff method. The present formulation can be implemented in acoustic pressure codes based on the Farassat's Kirchhoff formula for arbitrary moving bodies, thus allowing direct and fast calculation of the acoustic velocity field in scattering problems. For validation purposes, four test cases are considered, namely a three-dimensional monopole, dipole and quadrupole source, as well as a monopole in uniform flow. Comparison of the results with the analytical solutions proves the remarkable accuracy of the present formulation.