Convergence criteria for scattering models of ultrasonic wave propagation in suspensions of particles

Scattering models used to simulate the attenuation and phase velocity of an ultrasonic wave propagating through a suspension of particles involve the summation of an infinite series of partial waves. The accuracy of computation is influenced by the number of terms included in the harmonic series, and the number of terms required depends upon the scatterer size compared with wavelength. It is shown that the errors in modelled attenuation and phase velocity resulting from premature truncation can be significant when modelling higher values of particle diameter-frequency product. A useful and simple heuristic is presented, in which the number of terms in the summation of the infinite series needed for satisfactory convergence to a final value is a function of the particle diameter-frequency product and of the compressive wave velocity in the continuous phase.