On the use of Gegenbauer reconstructions for shock wave propagationmodeling

In therapeutic ultrasound, the presence of shock waves can be significantdue to the use of high intensity beams, as well as due to shock formation duringinertial cavitation. Although modeling of such strongly nonlinear waves can becarried out using frequency-domain methods, such calculations are typicallyconsidered impractical, since accurate calculations often require hundreds oreven thousands harmonics to be considered, leading to prohibitive computationaltimes. The use of Gegenbauer reconstructions as a postprocess tool to resolvethe band-limitations of the spectral methods are therefore investigated in thispaper. A three-dimensional transducer problems will be presented to validate theproposed method.