Abstract
Because of the complexities associated with the domain geometry and environments, accurate prediction of acoustics propagation and scattering in realistic shallow water environments by direct numerical simulation is challenging. Based on the pre-corrected Fast Fourier Transform (PFFT) method, we accelerated the classical boundary element method (BEM) to predict the acoustic propagation in a multi-layer shallow water environment. The classical boundary element method formulate the acoustics propagation problem as a linear equation system in the form of [A]{x}={b}, where [A] is an N×N dense matrix composed of influence coefficients. Solving such linear equation system requires O(N2/N3) computational cost for iterative/direct methods. The developed method, PFFT-BEM, can effectively reduce the computational efforts for direct numerical simulations from O(N2~3) to O(Nlog N), where N is the total number of boundary unknowns. To numerically simulate the sound propagation in a shallow water environment, we applied the first-order non-reflecting boundary condition in the truncated numerical domain boundary to eliminate the errors due to reflected waves. Multi-layer coupled formulation was used to include the environment inhomogeneity in PFFT-BEM. Through multiple convergence tests on the number of layers and elements, we validated and quantified the accuracy of PFFT-BEM. To demonstrate the usefulness and capability of the developed PFFT-BEM, we simulated three-dimensional (3D) underwater sound propagation through 3D geometries to check the efficacy of the established classical method: the 3D Parabolic equation model. Finally, PFFT-BEM was employed to simulate sound propagation through a complex multi-layer shallow water environment with internal waves. The “3D+T” results obtained by PFFT-BEM compared well with the physical test, thereby proving the capability and correctness of this method.
Highlights
The accurate forecasting of acoustics wave propagation and scattering in shallow water environments is important in naval operations and underwater communications
We have presented an efficient boundary element method with a multi-layer formulation and first-order non-reflecting boundary condition for the simulation of sound propagation in a shallow water environment
By using the pre-corrected fast Fourier transform method, the developed method, pre-corrected Fast Fourier Transform (PFFT)-boundary element method (BEM), which reduces the computational cost from O(N2 ) to O(Nlog N), can be applied to the 3D
Summary
The accurate forecasting of acoustics wave propagation and scattering in shallow water environments is important in naval operations and underwater communications. For direct numerical simulations (i.e., discretization methods without any assumptions), despite the continued development of computing capabilities, it is a challenge to perform 3D simulations of ocean acoustics in realistic environments due to the high computational costs. This induces a large computational cost and limits the use of BEM in real shallow water acoustics Another major drawback of BEM is that classical BEM can only formulate the linear equation system for underwater medium with homogeneous properties (e.g., density and sound speed). Using 3D+T PFFT-BEM (Version 2019, Massachusetts Institute of Technology, Cambridge, MA, USA, 2019), we simulate sound the change in medium properties caused by internal traveling waves, and we compare the numerical results with field tests
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