A new σ‐transform based Fourier‐Legendre‐Galerkin model for nonlinear water waves,International Journal for Numerical Methods in Fluids

当前位置： X-MOL 学术 › Int. J. Numer. Methods Fluids › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

A new σ‐transform based Fourier‐Legendre‐Galerkin model for nonlinear water waves
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-06-18 , DOI: 10.1002/fld.4881
Mathias Klahn ₁ , Per A. Madsen ₁ , David R. Fuhrman ₁

Affiliation

This paper presents a new spectral model for solving the fully nonlinear potential flow problem for water waves in a single horizontal dimension. At the heart of the numerical method is the solution to the Laplace equation which is solved using a variant of the

σ

‐transform. The method discretizes the spatial part of the governing equations using the Galerkin method and the temporal part using the classical fourth‐order Runge‐Kutta method. A careful investigation of the numerical method's stability properties is carried out, and it is shown that the method is stable up to a certain threshold steepness when applied to nonlinear monochromatic waves in deep water. Above this threshold artificial damping may be employed to obtain stable solutions. The accuracy of the model is tested for: (i) highly nonlinear progressive wave trains, (ii) solitary wave reflection, and (iii) deep water wave focusing events. In all cases it is demonstrated that the model is capable of obtaining excellent results, essentially up to very near breaking.

中文翻译：

基于σ变换的新型非线性水波Fourier-Legendre-Galerkin模型

本文提出了一种新的频谱模型，用于解决单个水平维度上水波的完全非线性势流问题。数值方法的核心是拉普拉斯方程的解，该解是使用

σ

-转变。该方法使用Galerkin方法离散化控制方程的空间部分，并使用经典的四阶Runge-Kutta方法离散化时间部分。对数值方法的稳定性进行了仔细的研究，结果表明，该方法在应用于深水非线性单色波时，在一定的阈值陡度下是稳定的。高于该阈值，可以采用人工阻尼以获得稳定的解决方案。对以下模型测试了模型的准确性：（i）高度非线性的渐进波列；（ii）孤波反射；（iii）深水波聚焦事件。在所有情况下，都证明该模型能够获得出色的结果，基本上可以达到非常接近断裂的效果。

更新日期：2020-06-18

点击分享查看原文

点击收藏

阅读更多本刊最新论文本刊介绍/投稿指南11