Split step wavelet Galerkin method based on parabolic equation model for solving underwater wave propagation

Authors:
Mostafa Bakhoday Paskyabi;Farzan Rashidi
Affiliations:
Control Research Department, Engineering Research Institute, Tehran, Iran;Control Research Department, Engineering Research Institute, Tehran, Iran
Venue:
WAMUS'05 Proceedings of the 5th WSEAS International Conference on Wavelet Analysis and Multirate Systems
Year:
2005

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Abstract

In this paper, split step wavelet Galerkin method (SSWGM) is proposed for solving underwater wave propagation in range-independent fluid/solid media. Parabolic equation model is applied for transforming elliptic wave to parabolic wave equation that enable us to use marching approaches in numerical algorithms. Wavelet Galerkin method is used to discretize the depth operators by using 1-periodic Daubechies scaling basis as shape functions. This discretization leads to circulant and bandlimit system which can be solved by fast Fourier transformations and this improves the accuracy and cost of computation. The numerical solution of SSWGM is applied for deep and shallow water environment involving water column over bottom. To evaluate the efficiency of the proposed method, some simulations are demonstrated and the usefulness of SSWGM is highlighted through them.