The causal impulse response for circular pistons in viscous media

Abstract

A causal impulse response for the Stokes wave equation is derived for calculations of transient pressure fields generated by circular pistons in viscous media. The causal Green’s function is numerically verified using the material impulse response function approach. The causal, lossy impulse response for a baffled circular piston is then calculated within the near-field and the far-field regions using expressions previously derived for the fast near-field method. Expressions for apodized pistons evaluated in the far-field region are also demonstrated. Transient pressure fields in viscous media are computed with the causal, lossy impulse response and compared to results obtained with the lossless impulse response. The numerical error in the computed pressure field is quantitatively analyzed for a range of viscous relaxation times and piston radii. Results show that the largest errors are generated in locations near the piston face and for large relaxation times, and errors are relatively small otherwise. These results suggest that this causal impulse response is ideal for time-domain calculations that simultaneously account for diffraction and frequency-dependent attenuation in viscous media. [This work was partially supported by NIH Grant 1R01 CA093669.]