高阶Boussinesq水波方程数值模型及其与实验结果的对比

本文建立了基于预报-校正差分格式的高阶Boussinesq方程数值模型，进行了有沙坝地形上非线性波浪传播的物理模型实验，检验了数值模型和高阶Boussinesq方程的精度。研究了非线性波浪在有沙坝地形上传播的特性，分析沙坝坡度和水深的影响。     

高阶非线性Boussinesq型方程及其数值验证

从Laplace方程和非线性的边界条件出发,通过将波动速度势函数表达为任意特定水深处的函数,推导了线性频散关系具有Airy波精确解的Padé[2,2]阶近似精度的高阶非线性的Boussinesq型方程。方程含有能量耗散项并完全满足水底边界条件。定性比较了高阶非线性方程和弱非线性方程的非线性特征。推导了二维四阶的滤波公式。建立了非线性波传播的数值模拟模型。结合两个具体算例,比较了数值模拟模型的强非线性版本和弱非线性版本的计算结果之间的差别,从而定量探讨了高阶非线性项对数值计算结果的影响。     

动量修正系数对恒定明渠流计算的影响

在采用浅水方程的洪水模拟中,经典的交替方向隐式格式(ADI)被认为不能用来计算跨临界流。这种格式会在自由水面和流速急剧变化的地方产生非物理振荡。然而,实际中这种格式仍然被广泛应用于商业计算软件。为了能够用ADI格式在模拟跨临界流时能够得到稳定的数值结果,修改动量修正系数(Boussinesq系数)这种数值处理方法能够部分地减轻ADI模型在模拟跨临界流时遇到的困难。该文通过对一维恒定流条件下的高速明渠流动问题的数值模拟,以及二维英国Boscastle地区洪水波的数值模拟,系统地评估了这种数值处理方法对模型计算的影响,并对比了ADI和具有激波捕捉能力的TVD-Mac Cormack模型的计算结果。结果表明,随着动量修正系数的减小,可以有效抑制ADI格式产生的数值振荡,但同时会降低水深的预测值。这些结果有助于评估数值格式在模拟跨临界流动时的准确性。     

基于WMLES方法的复式断面明渠三维紊流数值模拟

针对基于雷诺时均Navier-Stokes方程的数值模型在精确模拟复式断面明渠三维水流结构方面存在困难和传统大涡模拟(LES)方法计算成本相对较高的问题,采用壁面建模的大涡模拟(WMLES)方法建立三维数值模型,对水深比(滩地水深与主槽水深之比)为0.5的复式断面明渠水流结构进行模拟计算。数值模拟计算结果与已有试验测量结果和LES模拟结果的对比表明,WMLES方法能够准确地模拟时均速度、床面切应力、紊动强度、紊动能、雷诺应力分布、二次漩涡结构,该方法在复式断面明渠水流三维模拟中是可靠的;在保证计算精度的前提下,与传统LES方法相比,采用WMLES方法能够显著降低计算成本。     

沙坝海岸上裂流的数值模拟

建立了基于二阶完全非线性Boussinesq水波方程的二维波浪破碎数值模型,对沙坝海岸上产生的裂流进行了数值模拟研究。首先将文献[1]中给出的一组二阶完全非线性Boussinesq方程进行扩展,在动量方程中引入紊动粘性项模拟波浪破碎引起的能量耗散,采用窄逢法处理海岸动边界问题,并考虑了混合子网格效应以及水底摩擦。然后,在矩形网格上离散控制方程,采用有限差分方法和混合四阶Adams-Bashforth-Moulton预报矫正格式建立了数值模型。应用所建立模型对一带沟槽沙坝海岸上产生裂流的实验进行数值模拟,将计算的波高、增减水、时均流速、时均流场等与实验数据进行了比较。数值结果与实验结果吻合较好,这说明建立的数值模型是准确有效的,为下一步应用该模型模拟实际海岸上的裂流提供了研究基础。     

近岸波浪的Boussinesq型方程模拟及其应用

该文首先对近岸波浪数学模型的研究、发展、应用进行了回顾和总结,对各类波浪数学模型的特点进行了简单分析。基于改进的Boussinesq型方程建立了一个完整的近岸波浪数学模型,通过对方程的拓展,综合考虑了模型的造波、消波、动边界处理、波浪破碎等问题。拓展后的数学模型用P-C（预测-校正）法进行数值求解,计算效率高、稳定性好。采用两个经典地形试验数据对模型进行了的验证,数值结果和实验值吻合较好。最后,利用该模型进行了某渔港港池内波浪条件的数值模拟,给出了不同时刻港池内的波面情况,得到了合理的结果。     

系泊系统动力分析

对于海上定位采用的系泊系统,采用时域有限元法建立了缆索方程的数值模型。以单点系泊和多点系泊的模拟比较为例。对于单点系泊,通过给定上端点正弦运动,对锚泊线进行动力计算,与试验结果进行了比较。对于多点系泊,针对一Spar平台的张紧系泊系统进行了理论计算,并将计算得到的上端点张力时历及统计结果与相应的模型试验结果进行了比较。通过比较可以发现理论计算结果与模型试验结果吻合良好。该数值模型可用于不同水深下平台和系泊系统的耦合计算等。     

隧洞进口小水深引水系统调压井变态模型律研究

根据调压井和压力管道非恒定流的数学方程导出的模型律和模型比尺,指出了这些模型比尺在隧洞进口水深较小的调压系统模型试验中存在的问题,探讨了模型比尺在调压系统模型设计中的适应性,提出了隧洞进口水深较小时调压系统模型设计的原则。根据两个模型试验结果,通过理论计算和数值模拟可以看出,运用这些原则设计模型,试验结果与理论计算及数值模拟结果是一致的。     

一个模拟密度分层流特征的改进三维数值模型

为实现对强密度分层流的数值模拟,本文对Boussinesq近似及静压假设进行了讨论。并根据密度分层流的特点,在质量流量守恒条件下对通用POM模型的连续方程、动量方程及湍流模型方程进行了必要的改进。应用改进的三维数值模型,对两组盐度差下的分层流动进行了模拟。结果表明：在环境水体垂向密度变化不明显的情况下,采用静压假设是可取的。但对于环境水体存在明显密度分层的情况,由于垂向密度变化较大,静压假设并不适宜。相对原模型,改进模型得到的盐度等值线更加平稳,盐度垂向变化的梯度更大,计算结果更符合密度分层流的特征。     

新疆五一水库消力池悬栅消能水流水力特性数值模拟

采用RNGk-ε模型,利用VOF(Volume of Fluid)流体体积法追踪自由水面,对迪那河五一水库导流洞出口悬栅消力池内水流水力特性进行数值模拟,将计算的沿程水深、底部压强、流速与物理模型试验结果进行对比,计算值与实测值吻合较好。通过数值模拟研究,弥补了物理模型试验不足,为实际工程设计提供参考。     

A THIRD-ORDER BOUSSINESQ MODEL APPLIED TO NONLINEAR EVOLUTION OF SHALLOW-WATER WAVES

1.　INTRODUCTIONIncoastalandoceanengineering,thepredictionofwaverun-upwithadesirableaccuracyisoftenofparamountinterest.Previously,thesecond-orderBoussinesqmodel,whichassumesthatnonlinearanddispersiveeffectsarebothweakandofthesameorderofmagnitude,hasbeenextensivelyusedtostudytheevolutionofwavesinshallowwater(Peregrine,1967;MeiandUnliiata,1972etc.).Recently,theconventionalBoussinesqmodelhasalsobeenextendedtomodelwavesoveranintermediateorevenlargedepth,withinthescopeofasecond-ordertheory(wi…     

NUMERICAL SIMULATON OF IMPROVED BOUSSINESQ EQUATIONS BY A FINITE ELEMENT METHOD

1 .　INTRODUCTIONAswavespropagatetowardshore ,acombina tionofshoaling ,reflection ,refractionanddiffrac tioneffectsmodifythewaveform .Numericalmod elbasedonthetwo dimensionalBoussinesqequa tionshavebeenshowntobecapableofsimulatingthewavepropagationinthecoastalregionsaccu rately .ThestandardBoussinesqequationsderivedbyPeregrine[2 ] includethelowestordereffectsofnon linearityandfrequencydispersion .Becausetheerrorinthelineardispersionrelationincreaseswiththeincreaseofwaterdepth ,thestandar…     

Boussinesq 方程的高精度求解及其验证

本文采用高精度紧致差分格式提高浅水非线性的Boussinesq方程的求解精度，在未增加求解难度的前提下，建立了高精度、低耗散及较好线性色散性的数学模型。通过验证，表明非线性项求解精度的提高，使模型能更好地描述复杂地形上波浪的非线性变形，并能合理地模拟工程实际问题中的波浪折射、绕射、反射等物理现象。     

Revisiting study on Boussinesq modeling of wave transformation over various reef profiles

To better understand the complex process of wave transformation and associated hydrodynamics over various fringing reef profiles, numerical experiments were conducted with a one-dimensional （1D） Boussinesq wave model. The model is based on higher-order Boussinesq equations and a higher-accuracy finite difference method. The dominant energy dissipation in the surf zone, wave breaking, and bottom friction were considered by use of the eddy viscosity concept and quadratic bottom friction law, respectively. Numerical simulation was conducted for a wide range of wave conditions and reef profiles. Good overall agreement between the computed results and the measurements shows that this model is capable of describing wave processes in the fringing reef environment. Numerical experiments were also conducted to track the source of underestimation of setup for highly nonlinear waves. Linear properties （including dispersion and shoaling） are found to contribute little to the underestimation; the low accuracy in nonlinearity and the ad hoc method for treating wave breaking may be the reason for the problem.     

TESTS AND APPLICATIONS OF A BOUSSINESQ MODEL WITH AMBIENT CURRENT

A new type Boussinesq model is proposed and applied for wave propagation in a wave flume of uniform depth and over a submerged bar with current present or absent, respectively. Firstly, for the propagation of monochromatic incident wave with current absent, the Boussinesq model is tested in its complete form, and in a form without the introduction of utility velocity variables. It is validated that the introduction of utility velocity variables can improve the characteristics of velocity field, dispersion and nonlinearity. Both versions of the Boussinesq models are of higher accuracy than the fully-nonlinear fourth-order model, which is one of the best forms among the existing traditional Boussinesq models that do not incorporate breaking mechanism in one dimension. Secondly, the Boussinesq model in its complete form is applied to simulating the propagation of bichromatic incident waves with current present or absent, respectively, and the modeled results are compared to the analytical ones or the experimental ones. The modeled results are reasonable in the case of inputting bichromatic incident waves with the strong opposing current present.     

Numerical simulation of wave transformation,breaking and runup by a contravariant fully non-linear Boussinesq equations model

In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations(FNBE) in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-finite difference scheme. A high-order upwind weighted essentially non-oscillatory(WENO) finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations(NSWE). On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento(Italy).     

应用Boussinesq方程对非线性Stem波的数值研究

本文应用具有四阶频散特征的新型Ｂｏｕｓｓｉｎｅｓｑ方程，采用空间差分为交错Ｓｈｕｍａｎ格式，时间层为ＡＤＩ的有限差分格式，对非线性Ｓｔｅｍ波进行了数值模拟研究。其结果表明，这种组合式差分格式能有效地模拟非线性Ｓｔｅｍ波的演变规律。同时由计算结果也发现当入射波质的角大于某临界值时，Ｓｔｅｍ波动场向Ｇｅｎｕｓ－２波系转化并呈现出较稳定的六角形波型双周期结构，在入射波系的入射角小于某一临界值时，沿墙发展     

COMPARISON BETWEEN BOUSSINESQ EQUATIONS AND MILD-SLOPE EQUATIONS MODEL

1. INTRODUCTIONWave transformation,one of the most i mpor-tant near-shore hydrodynamic processes , has closerelations to human activities as well as i mpact on o-ceanic environment , resources and engineeringstructures .So it is of greater i mportance to …     

热分层湍流直接模拟的高精度算法和数值分析

该文发展了高阶精度有限差分格式的直接数值模拟方法,并将其成功地应用于带有自由面的热分层槽道湍流问题的计算,与低阶精度格式相比,高精度格式有着更宽的低耗散波段,对中高波数分量有较好的模拟能力。该文直接在非均匀网格上采用Lagrange多项式插值构造迎风偏置格式,克服了传统二阶格式在网格变化剧烈时精度损失的缺点,提高了在近壁区的计算精度。对三维槽道湍流以及带有自由面的热分层湍流的流场和温度场的统计特征、脉动特征以及能谱进行了分析,进一步验证了高精度差分方法对热分层剪切湍流问题直接模拟的有效性。总体上讲,该格式精度高,对高频非物理振荡有抑制作用,可以适应变化的空间网格,有效地模拟复杂湍流流动结构,并正确地揭示其流动机理.     

NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP

Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.