An iterative three-dimensional parabolic equation solver for propagation above irregular boundaries

Area of Science:

• Atmospheric acoustics
• Computational physics
• Geophysical fluid dynamics

Background:

• Accurate modeling of sound propagation is essential for understanding atmospheric phenomena.
• Existing two-dimensional models struggle with complex topography and atmospheric refraction.
• Infrasound propagation is significantly influenced by three-dimensional environmental factors.

Purpose of the Study:

• To develop and validate an iterative three-dimensional parabolic equation solver.
• To incorporate irregular terrain and atmospheric stratification effects.
• To enhance the accuracy of infrasound propagation simulations in complex environments.

Main Methods:

• Applied a terrain-following coordinate transformation (Beilis-Tappert mapping) to the narrow-angle parabolic equation.
• Discretized the problem using the Crank-Nicolson scheme and second-order finite-differences.
• Utilized an efficient iterative fixed-point solver involving tridiagonal matrix inversions.

Main Results:

• The 3D solver accurately accounts for boundary conditions and atmospheric refraction.
• Transversal scattering effects in the shadow zone of obstacles were identified.
• The 3D model showed improved accuracy over 2D models, particularly in underestimating pressure amplitude.

Conclusions:

• The developed iterative 3D parabolic equation solver is suitable for simulating infrasound propagation.
• The model effectively handles realistic topographies and layered atmospheres.
• This advancement is critical for accurate infrasound monitoring and analysis in complex terrains.