Pressure distribution analysis of focused shock wave by using finite element method

The aim of this study is to analyze the generated pressure by the focusing of a shock wave and to verify that the focal point has the smallest width of the wavefront and the maximum pressure value. The study was achieved by simulation using the finite element method because it allows us to obtain a numerical solution at any point in the considered domain. It was necessary to consider a specific geometry to achieve the focusing of a shock wave; in this case a semi-ellipse was used. When a shock wave is generated in a semi-ellipse, a part of the wave is transmitted and the remaining wave is reflected. The part of the wave that is reflected on the surface of the semi-ellipse focuses later at a focal point while the width of its waveform is reduced and its pressure increases. The non-reflected wave, looses pressure and scatters as it travels away from the semi-ellipse. Furthermore, the pressure obtained during the trajectory of the non-reflected wave is not zero and may damage surrounding materials, like organs in a lithotripsy treatment, by the focal point.