This study presents a comprehensive numerical investigation of thermoacoustics (TA) wave propagation in the time domain using the Finite Difference Time Domain (FDTD) method, with a comparative analysis against the k-space pseudospectral approach. The TA wave equation is modeled under the assumptions of homogeneous, lossless, and isotropic medium, incorporating a physically realistic source term. A Gaussian initial pressure distribution is employed as the primary excitation, and the resulting acoustic signals are recorded using point and multi-sensor configurations. The study systematically the influence of spatial grid resolution and the Courant-Friedrichs-Lewy (CFL) number on numerical stability and accuracy. It is observed that maintaining a constant CFL number ensures consistent wave propagation behavior across different grid resolutions, whereas variations in CFL lead to significant discrepancies in amplitude and phase of the propagated signals. In addition to Gausian sources, various realistic source geometries, including circular disk, Chebyshev polynomial-based, and asymmetric (rock-like) distributions, are investigated to analyze their impact on wavefield characteristics. The numerical results demonstrate strong agreement between the FDTD and k-space method in both time and frequency domains under stable conditions. However, deviations are observed at higher frequencies due to numerical dispersion effects, particularly in the FDTD scheme. Furthermore, it is shown that sharp discontinuities in binary image based sources introduce non-physical high-frequency components, resulting in spurious oscillations. This study highlights the importance of numerical parameter selection, particularly the CFL condition, and provides a detailed comparision of two widely used computational methods for TA wave simulation. The findings offer valuable insights into the role of source geometry and numerical schemes in accurately modeling acoustic wave propagation.
Ujjal Mandal (Thu,) studied this question.