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On the use of Gegenbauer reconstructions for shock wave propagation modeling

In therapeutic ultrasound, the presence of shock waves can be significant due to the use of high intensity beams, as well as due to shock formation during inertial cavitation. Although modeling of such strongly nonlinear waves can be carried out using frequency-domain methods, such calculations are typically considered impractical, since accurate calculations often require hundreds or even thousands harmonics to be considered, leading to prohibitive computational times. The use of Gegenbauer reconstructions as a postprocess tool to resolve the band-limitations of the spectral methods are therefore investigated in this paper. A three-dimensional transducer problems will be presented to validate the proposed method.