A Time-Domain Wavenumber Integration Model for Underwater Acoustics Based on the High-Order Finite Difference Method
Abstract
:1. Introduction
2. Time-Domain Wavenumber Integration Model
2.1. Hankel Transform of the Wave Equation
2.2. Wavenumber Discretization
3. The FDM for Solving the Depth Equation
3.1. Temporal Discretization
3.2. Spatial Discretization
3.2.1. Interior Point Schemes
3.2.2. Boundary Schemes
3.2.3. Interface Schemes
3.3. Source Treatment Method
4. Test Cases
4.1. Lloyd’s Mirror
4.2. Ideal Waveguide
4.3. Head Wave
4.4. Computation Analysis
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Do j = 2, NTot1 − 1! The number of interior points U2(j) = AD1(j) * U1(j) + AE1(j) * U1(j − 1) + AE1(j + 1) * U1(j + 1) + AD0(j) * U0(j) + AE0(j) * U0(j − 1) + AE0(j + 1) * U0(j + 1) End do ! U0 denotes the kernel function at the previous time step ! U1 denotes the kernel function at the current time step ! U2 denotes the right-hand side ! AD0 denotes the diagonal element of the previous time step coefficient matrix ! AE0 denotes the off-diagonal element of the previous time step coefficient matrix ! AD1 denotes the diagonal element of the current time step coefficient matrix ! AE1 denotes the off-diagonal element of the current time step coefficient matrix |
Cases | FEM-2nd (PPW = 20) | FDM-4th (PPW = 20) | FDM-4th (PPW = 15) |
---|---|---|---|
Lloyd’s mirror | 16.310 s | 19.547 s | 14.120 s |
Ideal waveguide | 2.712 s | 3.185 s | 2.373 s |
Head wave | 20.116 s | 24.506 s | 17.336 s |
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Xu, X.; Liu, W.; Xu, G. A Time-Domain Wavenumber Integration Model for Underwater Acoustics Based on the High-Order Finite Difference Method. J. Mar. Sci. Eng. 2024, 12, 728. https://doi.org/10.3390/jmse12050728
Xu X, Liu W, Xu G. A Time-Domain Wavenumber Integration Model for Underwater Acoustics Based on the High-Order Finite Difference Method. Journal of Marine Science and Engineering. 2024; 12(5):728. https://doi.org/10.3390/jmse12050728
Chicago/Turabian StyleXu, Xiang, Wei Liu, and Guojun Xu. 2024. "A Time-Domain Wavenumber Integration Model for Underwater Acoustics Based on the High-Order Finite Difference Method" Journal of Marine Science and Engineering 12, no. 5: 728. https://doi.org/10.3390/jmse12050728
APA StyleXu, X., Liu, W., & Xu, G. (2024). A Time-Domain Wavenumber Integration Model for Underwater Acoustics Based on the High-Order Finite Difference Method. Journal of Marine Science and Engineering, 12(5), 728. https://doi.org/10.3390/jmse12050728