Self-adaptive absorbing boundary conditions for quasilinear acoustic wave propagation

We propose a self-adaptive absorbing technique for quasilinear ultrasound waves in two- and three-dimensional computational domains. As a model for the nonlinear ultrasound propagation in thermoviscous fluids, we employ Westervelt's wave equation solved for the acoustic velocity potential. The angle of incidence of the wave is computed based on the information provided by the wave-field gradient which is readily available in the finite element framework. The absorbing boundary conditions are then updated with the angle values in real time. Numerical experiments illustrate the accuracy and efficiency of the proposed method.