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Three-dimensional Cartesian parabolic equation model with higher-order cross-terms using operator splitting, rational

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A new numerical method efficiently models underwater sound propagation using the acoustic parabolic equation. This algorithm improves accuracy and stability for 3D ocean acoustics.

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Area of Science:

  • Ocean acoustics
  • Computational physics
  • Numerical modeling

Background:

  • Accurate modeling of sound propagation is crucial for underwater applications.
  • Existing methods for the acoustic parabolic equation face challenges in 3D environments.
  • Efficient and stable algorithms are needed for complex ocean geometries.

Purpose of the Study:

  • To develop an efficient, approximate three-dimensional Cartesian split-step marching solution for the acoustic parabolic equation.
  • To enhance the algorithm's applicability for sound propagation modeling in 3D oceans.
  • To address numerical stability and accuracy issues in complex underwater environments.

Main Methods:

  • Utilized operator splitting to decompose the acoustic parabolic equation's exponential operator.
  • Implemented split-step Padé algorithm for depth and cross-range operators.
  • Applied a rational filter (rectangular type) to stabilize Taylor series expansion for depth and cross-range operators.

Main Results:

  • The proposed split-step marching solution offers an efficient algorithm for 3D sound propagation.
  • The rational filter enhances solution stability, albeit with increased computational cost.
  • Numerical performance was evaluated and illustrated within an ocean wedge environment.

Conclusions:

  • The developed approximate Cartesian split-step marching solution provides an efficient approach for 3D acoustic propagation.
  • The integration of a rational filter improves model stability, crucial for complex ocean environments.
  • Further analysis confirmed the model's accuracy, efficiency, and stability in realistic scenarios.