一种新型二阶全非线性Boussinesq方程及其数值验证

通过改进二阶全非线性 Boussinesq 波浪方程中的色散项,得到了一组没有改变原方程的数学形式但适用于更大变化水深的新方程,其色散性能和变浅性能都比原方程有了很大改进,所适用的水深范围更大,能更好地描述从深水到近岸浅水处的波浪传播;并基于新方程建立了波浪数值模型,通过模拟波浪从浅水到深水的传播变形来验证新方程的有效性.     

Boussinesq方程波浪数学模型的应用

介绍了Ｂｏｕｓｓｉｎｅｓｑ 方程的推导过程和发展过程,基于深水和缓变地形的色散关系,建立了Ｂｏｕｓｓｉｎｅｓｑ方程的波浪数学模型。该模型可以产生波浪,模拟吸收边界和不同反射率的反射边界。该模型可用于研究深水和浅水地区波浪的浅水变形、折射、绕射和反射     

Numerical Simulation of Abnormal Wave Height Change Induced by Excavated Waterway with Boussinesq Equation

A nonlinear numerical model has been set up by use of Boussinesq Equation with finite differ-ence method,and has been applied to the simulation of the abnormal change of wave height induced by ex-cavated waterway.Numerical results demonstrate that the abnormal change of wave height is due to theadding of the reflected wave height induced by excavated waterway to the incident wave height.Becausethe angle between the incident wave and the axis of the waterway is smaller than the critical angle,the re-flected wave produced by the waterway may propagate to the breakwater and may be added with the inci-dent wave,then the abnormal change of wave height before the breakwater may be caused.So the wave re-flection caused by the change of water depth cannot be neglected.     

A Boussinesq Equation-Based Model for Nearshore Wave Breaking

Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally‘ s analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.     

The New Form of Time-Dependent Mild Slope Equation for Random Waves

The mild-slope equation derived by Berkhoff (1972), has widely been used in the numerical calculation of refraction and diffraction of regular waves. However, it is well known that the random sea waves has a significant effect in the refraction and diffraction problems. In this paper, a new form of time-dependent mild slope equation for irregular waves was derived with Fade approximation and Kubo's time series concept. The equation was simplified using WKB method, and simple and practical irregular mild slope equation was obtained. Results of numerical calculations are compared with those of laboratory experiments.     

一种基本Boussinesq方程的近岸区破碎波模型

基于文献「１」Ｂｏｓｓｉｎｅｓｑ方程的近岸区破碎波模型基础,将数值模型中的波高衰减规律由假设改进为Ｄａｌｌｙ的解析公式,使近岸区破碎波模型的应用性更强。并将数值模型计算结果与现场实验资料进行对比,取得了满意的结果。     

Boussinesq方程与抛物型缓坡方程2种波浪模型的比较分析

波浪破碎的模拟对于波浪模拟的准确性十分重要。为了解波浪破碎模型的问题,本文对抛物型缓坡方程和Boussinesq方程这2种波浪模型所采用的破碎方法进行比较和分析。运用基于Boussinesq方程的Funwave模型和基于抛物型缓坡方程的REF/DIF模型,分别对特拉华大学的未破碎圆形浅滩试验和作者于实验水槽进行的Undertow试验这2个物理模型进行波高模拟、比较与分析。模拟结果表明:Funwave和REF/DIF这2种波浪模型都能准确的模拟出波高随水深的变化情况,但对于波浪破碎后的情况,REF/DIF模型模拟的更为精确一些。     

基于完全非线性Boussinesq方程的源函数数值造波

探讨了应用于完全非线性Boussinesq模型模拟波浪传播变形的数值造波和波浪分析方法。采取在造波区的流体运动方程中引入源函数的造波法以实现无反射造波。通过数值试验探讨了造波函数中系数δ的取值。为模拟不规则波,采用了线性波浪叠加法。利用相关函数法进行谱估计,以检验不规则波造波效果。文中讨论了采用相关函数法估计海浪谱时,参数△t、m、和N之间的关系。     

不规则波Boussinesq型方程的造波,消波和反射

对前人提出的造波、消波和反射边方法分析表明,其方法是极浅水波近似,不适用于任意水深的水域,本文就任意水深变化Ｂｏｕｓｓｉｎｅｓｑ型方程,提出了不规则波新的造波原理、方法和消波边界及部分反射边界波动方程,试验表明,本文提出的造波、消波和反射方程有效而可靠的。     

Numerical Calculation for Nonlinear Waves in Water of Arbitrarily Varying Depth with Boussinesq Equations

Based on the high order nonlinear and dispersive wave equation with a dissipalive term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/ L0≤ 1. By the application of the completely implicit slagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.     

用含高色散性Boussinesq方程模拟潜堤上的波浪变形

基于一种高阶Boussiensq方程(刘忠波等,2004),采用预报-校正格式的有限差分法对该方程进行了数值离散,建立了数值模型。针对动量方程中三阶项的差分形式,采用了迎风格式和五点格式。通过数值模拟常水深下不同周期波浪传播变形,指出迎风格式在计算小周期波浪时存在的问题。为进一步验证数值模型的适用性,模拟了淹没潜堤上的传播变形。从数值结果与实验值的对比结果上看,该数值模型能较好地模拟波浪变形,可用于模拟实际中的波浪场问题。     

基于双层Boussinesq方程的三维波浪数值模型及其验证

Liu等给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。     

A new form of higher order Boussinesq equations

On the basis of the higher order Boussinesq equations derived by the author (1999), a new form of higher order Boussinesq equations is developed through replacing the depth-averaged velocity vector by a new velocity vector in the equations in order to increase the accuracy of the linear dispersion, shoaling property and nonlinear characteristics of the equations. The dispersion of the new equations is accurate to a [4/4] Pade expansion in kh. Compared to the previous higher order Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling property of the equations have higher accuracy from shallow water to deep water.     

A Compact Explicit Difference Scheme of High Accuracy for Extended Boussinesq Equations

Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations.For time discretization,a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage,a cubic spline function is adopted at correcting stage,which made the time discretization accuracy up to fourth order;For spatial discretization,a three-point explicit compact difference scheme with arbitrary order accuracy is employed.The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme.The numerical results agree well with the experimental data.At the same time,the comparisons of the two numerical results between the present scheme and low accuracy difference method are made,which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations.As a valid sample,the wave propagation on the rectangular step is formulated by the present scheme,the modelled results are in better agreement with the experimental data than those of Kittitanasuan.     

航道对多方向波传播影响

应用Boussinesq方程对不同入射角、不同方向集中度的波浪与航道的相互作用进行模拟,得到了航道的折射影响规律以及不同入射角、不同方向集中度的波浪对航道作用的差别.结果对试验研究及工程实践有指导意义.     

A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast.     

Nonlinear Dispersion Relation in Wave Transformation

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Boussinesq相位解析的海岸水动力学数学模型研究进展

由于在平衡计算效率和精度上具有优势,Boussinesq相位解析数学模型研究不断取得突破,已成为波浪和水流精细化模拟的较优解析方式,为海岸工程、环境、地质等问题提供了实用和高效的研究手段。本文对已有Boussinesq类模型的研究进行了评述,深入探讨其重要发展、实际应用和理论瓶颈,从高阶非静压修正、GPU准三维高性能算法编译、波浪破碎和泥沙运移沉积等4个方面提出未来可能的科学突破方向。     

近岸波浪在刚性植被区域传播的数值模型

基于扩展型Boussinesq水波方程,建立了波浪在刚性植被覆盖的近岸海域传播的数值模型。通过在动量方程源项中引入拖曳阻力项考虑植被对波浪的衰减作用。控制方程采用有限差分和有限体积混合格式求解,模型稳定性强,具备间断捕捉能力,能有效模拟近岸区域波浪的传播变形、破碎和处理海岸动边界问题。利用所建立模型对典型物理模型实验进行模拟,计算结果与实验结果吻合良好,表明模型可用于波浪在刚性植被覆盖海域的数值计算。     

Numerical Models of Higher-Order Boussinesq Equations and Comparisons with Laboratory Measurement

Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of two different wave propagation models has been investigated. One is higher-order Boussinesq equations derived by Zou (1999) and the other is the classic Boussinesq equations. Physical experiments are conducted, three different front slopes (1:10, 1:5 and 1:2) of the shelf are set up in the experiment and their effects on wave propagation are investigated. Comparisons of numerical results with test data are made, the model of higher-order Boussinesq equations agrees much better with the measurements than the model of the classical Boussinesq equations. The results show that the higher-order Boussinesq equations can also be applied to the steeper slope case although the mild slope assumption is employed in the derivation of the higher order terms of higher order Boussinesq equations.