Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach

Ujjal Mandal

doi:doi:10.11648/j.ajmp.20261503.12

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Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach

Ujjal Mandal^*

Published in American Journal of Modern Physics (Volume 15, Issue 3)

Received: 26 March 2026 Accepted: 8 April 2026 Published: 7 May 2026

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Abstract

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.

Published in	American Journal of Modern Physics (Volume 15, Issue 3)
DOI	10.11648/j.ajmp.20261503.12
Page(s)	77-85
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Finite Difference, Isotropic Medium, Thermoacoustic, Courant-Friedrichs-Lewy Number

References

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APA Style

Mandal, U. (2026). Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach. American Journal of Modern Physics, 15(3), 77-85. https://doi.org/10.11648/j.ajmp.20261503.12

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ACS Style

Mandal, U. Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach. Am. J. Mod. Phys. 2026, 15(3), 77-85. doi: 10.11648/j.ajmp.20261503.12

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AMA Style

Mandal U. Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach. Am J Mod Phys. 2026;15(3):77-85. doi: 10.11648/j.ajmp.20261503.12

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@article{10.11648/j.ajmp.20261503.12,
  author = {Ujjal Mandal},
  title = {Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach
},
  journal = {American Journal of Modern Physics},
  volume = {15},
  number = {3},
  pages = {77-85},
  doi = {10.11648/j.ajmp.20261503.12},
  url = {https://doi.org/10.11648/j.ajmp.20261503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20261503.12},
  abstract = {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.
},
 year = {2026}
}

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TY  - JOUR
T1  - Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach

AU  - Ujjal Mandal
Y1  - 2026/05/07
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmp.20261503.12
DO  - 10.11648/j.ajmp.20261503.12
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 77
EP  - 85
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20261503.12
AB  - 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.

VL  - 15
IS  - 3
ER  -

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Author Information

Ujjal Mandal

Department of Applied Physics, Indira Gandhi National Open University, New Delhi, India

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http://orcid.org/0009-0008-3559-0502

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APA Style

Mandal, U. (2026). Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach. American Journal of Modern Physics, 15(3), 77-85. https://doi.org/10.11648/j.ajmp.20261503.12

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ACS Style

Mandal, U. Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach. Am. J. Mod. Phys. 2026, 15(3), 77-85. doi: 10.11648/j.ajmp.20261503.12

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AMA Style

Mandal U. Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach. Am J Mod Phys. 2026;15(3):77-85. doi: 10.11648/j.ajmp.20261503.12

Copy | Download

@article{10.11648/j.ajmp.20261503.12,
  author = {Ujjal Mandal},
  title = {Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach
},
  journal = {American Journal of Modern Physics},
  volume = {15},
  number = {3},
  pages = {77-85},
  doi = {10.11648/j.ajmp.20261503.12},
  url = {https://doi.org/10.11648/j.ajmp.20261503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20261503.12},
  abstract = {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.
},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Numerical Simulation of Time Domain Thermoacoustic Wave Equation Using the FDTD Method with Comparison to the k-Space Pseudospectral Approach

AU  - Ujjal Mandal
Y1  - 2026/05/07
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmp.20261503.12
DO  - 10.11648/j.ajmp.20261503.12
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 77
EP  - 85
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20261503.12
AB  - 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.

VL  - 15
IS  - 3
ER  -

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