Shock wave propagation with the KZK equation
Numerical methods that solve the nonlinear parabolic wave (KZK) equation and satisfy the Rankine-Hugoniot relation for shock wave propagation at all attenuation strengths are described and characterized. By comparison with a known planar solution, it is demonstrated that current numerical methods in the time domain predict a shock front that is stationary relative to the propagation phase in the inviscid case and that the proposed method predicts the correct speed. These methods are then compared in the context of shock wave lithotripsy and high intensity focused ultrasound. At the focus, axisymmetric shock wave lithotripter simulations show that the proposed methods predict peak positive pressures that are 20% smaller, peak negative pressures that are 10% larger, and a full width half maximum that is 45% larger. High intensity focused ultrasound simulations for an axisymmetric transducer in water have even larger variations in peak positive pressures and intensity but smaller variations in peak negative pressure. Simulations from a rectangular transducer in tissue, where absorption is more prominent, exhibit smaller but significant variations in peak pressures and intensity. © 2006 IEEE.
