FDTD analysis of TA waves
DOI:
https://doi.org/10.62059/LatArXiv.preprints.689Keywords:
Finite difference, Isotropic medium, Thermoacoustic, Courant-Friedrichs-Lewy numberAbstract
This study presents the numerical simulation of thermoacoustic (TA) wave propagation in time domain using the Finite Difference Time Domain (FDTD) method, along with a comparative analysis against the k-Space pseudospectral method (k-Wave). A physically realistic thermoacoustic source is modeled using a Gaussian initial pressure distribution, and the resulting pressure signals are recorded using a point sensor. The numerical results obtained from both methods show excellent agreement for different grid resolutions when a fixed Courant-Friedrichs-Lewy (CFL) number is maintained. However, discrepancies arise when different CFL numbers are used for varying grid resolutions, leading to mismatched signal responses. Further investigations are conducted using various realistic source configurations, including circular (disk), Chebyshev polynomial based ($1^{st}$ order), and asymmetric (rock-like) shapes. The corresponding time domain signals and frequency spectra are analyzed using both FDTD and k-space methods. It is observed that the two methods exhibit strong agreement in the low frequency regime, while noticeable deviations occur at higher frequencies. Further the study highlights the limitations associated with binary image based sources. Sharpe discontinuities at the edges introduces non-physical high frequency components, resulting in spurious oscillations and degraded signal quality. A multi sensor configuration is utilized to analyze the signals at different locations.
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