A New Method to Calculate the Wave Height of Deformed Shallow Water Based on the Gauss Global Radial Basis Function
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摘要: 应用Gauss全局径向基函数来模拟波浪浅水变形波高变化方程中的未知函数,经实例分析探讨得到了一种可用于求解该方程数值解的新方法,并将其计算结果与常用数值分析方法得到的数值解相互对比印证,证明了基于Gauss全局径向基函数法计算结果的正确性.经验证,Gauss径向基函数法的平均计算误差相比其他方法均要小,表明该方法拥有更高的计算精度.同时,根据Gauss全局径向基函数的逼近结果,得出了浅水变形波高变化微分方程数值解的拟合函数,在实际工程中,可以利用该拟合函数来代替原方程的解析解,研究成果可为求解近岸浅水区域波浪运动提供一种新思路.
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关键词:
- Gauss全局径向基函数(GRBF) /
- 浅水变形 /
- 波高变化方程 /
- 数值解
Abstract: The Gauss global radial basis function (GRBF) was used to simulate the unknown function of the changing wave height differential equation for shallow water deformation. Through a case analysis a new GRBF method was built to obtain the numerical solution of this equation in the conditions of laminar as well as turbulent boundary layers, and the GRBF calculation results were compared with those from the traditional numerical methods. The average calculation error of the GRBF method is smaller than that of the other methods, which indicates higher calculation accuracy of the proposed method. Meanwhile, based on the GRBF approximation results, a fitting function to the numerical solution of the wave height differential equation for deformed shallow water was formulated and intended to replace the corresponding intangible analytical solution in engineering application. The work provides a new way to study the wave motion in the coastal shallow water areas. -
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