Numerical Analysis of Long Range Sound Wave Propagation in Ocean by Wave Equation Finite Difference Time Domain Method with Graphics Processing Unit

Abstract

The wave equation finite difference time domain (WE-FDTD) method is applied to the analysis of the long range sound wave propagation in the deep ocean. In the WE-FDTD method, the wave equation in the cylindrical coordinate is directly discretized on the basis of the central differences. The method is then implemented on a graphics processing unit (GPU) cluster system, which consists of 32 GPUs. Assuming the axisymmetric field, two-dimensional numerical models whose region size is 1000 km × 5000 m are developed for various cell sizes (1–3 m). Some numerical demonstrations are made for sound wave propagation in the deep ocean under the assumption of the Munk profile, which is known as the sound speed profile of the mid-latitude of the Pacific Ocean. The numerical results are compared with the results obtained using the ray-tracing method. It is found that the numerical dispersion error appears strikingly in the WE-FDTD solutions when the points per wavelength are less than 20 p.p.w., while the WE-FDTD solutions show good agreement with the ray-tracing solutions in the propagation time when the points per wavelength are more than 20 p.p.w. It is confirmed that the WE-FDTD method can be applied to the analysis of long range sound wave propagation in the deep ocean with reasonable accuracy.