Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves.

Cihan Bayındır

doi:10.1038/srep22100

Abstract

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions.

Highlights

The signals, with majority of the components are zero, are called sparse signals
Performing time integration with smaller number of spectral components and using the compressive sampling technique, it shown that the ocean wave field can be modeled with a significantly better efficiency compared to the classical spectral method
The two methods are in excellent agreement as it can be seen in the figure

Summary

Introduction

The signals, with majority of the components are zero, are called sparse signals. Like majority of the signals in the nature, the ocean waves are sparse either in the time or in the frequency domain. The compressive sampling technique can be thought as a very efficient tool for measuring or simulating the ocean waves. In this paper it is shown that the efficiency of the compressive sampling technique can be used for the improvement of the computational simulation efforts of the ocean waves. Performing time integration with smaller number of spectral components and using the compressive sampling technique, it shown that the ocean wave field can be modeled with a significantly better efficiency compared to the classical spectral method. It is shown that by using a smaller number of spectral components and the compressive sampling technique, ocean waves can be simulated very efficiently compared to the classical spectral simulation with a larger number of spectral components. It is shown that the proposed compressive spectral method can be a very efficient tool in simulations of fully nonlinear ocean waves

Methods

Results

Conclusion