Modeling of transient ultrasonic wave propagation using the distributed point

Transient ultrasonic waves in a fluid medium generated by a flat circular and a point-focused transducer of finite size are modeled by the distributed point source method (DPSM). DPSM is a Green's-function-based semi-analytical mesh-free technique which is modified here to incorporate the transient loading from a finite-sized acoustic transducer. Conventional DPSM solves acoustic problems in steady-state frequency domain. Here, DPSM is extended to the time domain without the fast Fourier transform (FFT) but using the Green's function in the time domain. This modified method is denoted t-DPSM. Harmonic point sources of DPSM are replaced by time-dependent point sources in t-DPSM. Generated t-DPSM results are compared with the finite element (FE) results for both focused and flat circular transducers. The developed method is used to solve the transient problem of wave scattering by an air bubble in a fluid as the bubble is moved horizontally or vertically from the focal point of the focused transducer. The received energy signal is compared for different eccentricities.