Noniterative second harmonic ultrasound field simulations: an axisymmetric approach

Nonlinear numerical modeling of finite amplitude acoustic beams has a key role in understanding the effects of nonlinearities and in the design of state-of-art ultrasonic systems. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is the most accurate model describing the combined effects of diffraction, absorption and nonlinearity in ultrasound wave propagation. KZK solutions usually follow two different approaches: the spectral method and the time domain method; the first one is well suited for periodic ultrasound excitation, while the second is more efficient in propagation of short pulses. As finite difference methods and stepping techniques are usually employed in most realizations, prediction accuracy and computational burden of arbitrary depth ultrasound field simulations are strongly related to the depth itself. The work described in this report points to develop a model for simulating second harmonic ultrasound fields while featuring equations that can be solved without the use of iterative techniques. By using a proper domain change and dealing with the integration in the axial direction with a proper approximation, robust estimations of nonlinear sound fields are produced for both focused and unfocused axisymmetrical sources. Predicted fields profiles for nonlinear propagation in water from real transducers will be presented and compared with measurements from water tank experiments.