Numerical study of low-frequency sound beams

This paper is concerned with study of low-frequency sound beams generated as difference-frequency secondary field in parametric array. As model equations for theoretical investigation, KZK equation and Higher-order parabolic equation (HOPE) [Kamakura, T., Masahiko, A., Kenicii, A, Acoust. Sci. & Tech. 25, 2, (2004)] were used. Efficient numerical algorithm capable of massive parallelization was proposed for numerical integration of the model equations. Numerical results obtained using KZK equation and HOPE show that the KZK equation overestimates amplitude of the difference-frequency secondary wave in the near-field of the primary wave at the axis of symmetry. Both the equations provide the same results in the far-field and at the off-axis for both low- and high-frequency secondary fields.