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1.
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。 相似文献
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非线性波浪波面追踪的一种新模式 总被引：1，自引：0，他引：1
基于Laplace方程的Green积分表达式和波面BemouUi方程所建立的非线性波动数学模型,是一个时域上具有初始值的边值问题,而精确地追踪自由表面的波动位置,给出波面运动瞬时的波面高度和波面势函数,是建立时域内非线性波浪数值模式的基础。本文采用0-1混合型边界元剖分计算域边界并离散Laplace方程的Green积分表达式,采用有限元剖分自由水面并推导满足自由表面非线性边界条件的波面有限元方程,联立计算域内以节点波势函数和波面位置高度的时间增量为未知量的线性方程组,通过时步内的循环迭代,给出每个时步上的波面位置和波面势函数,从而建立了一种新的非线性波浪波面追踪模式。数值造波水槽内的波浪试验表明,其数值模拟结果具有良好的计算精度。 相似文献
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探讨一种基于完全非线性Boussinesq方程的波浪破碎模型在沿岸流计算中的应用问题。针对控制方程中的完全非线性项对沿岸流成长过程的影响进行了深入讨论。数学模型计算结果表明,完全非线性项有使平均流局部化的作用;通过数模实验还发现,垂向高阶涡度项可以有效抑制破波区外回流;运用Visser的实验室沿岸流实测资料从沿岸流速度、波高和平均水位几方面对所提模型进行了验证,并给出了紊动参数的计算结果。 相似文献
4.
系泊船非线性波浪力时域计算: 二维模型 总被引：6，自引：1，他引：6
为找到具有工程实用价值的港口系泊船波浪力的时域计算方法,建立了在港口中存在系泊船时非线性波浪力时域计算的垂直二维耦合模型:用Boussinesq方程计算船的两侧的外域,用欧拉方程计算船底面下的内域,两域在交界面处的连接条件是流量连续和压力相等.将复平面内的边界元方法应用于所研究问题,对耦合模型进行了验证.进行了相关模型实验,实验结果与数值计算结果比较表明这两种数值计算模型都具有满意的精度,但耦合模型的计算效率要远远高于边界元方法的计算效率.本耦合模型的数学处理简单,可适用于工程计算. 相似文献
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该文采用化为积分方程组的方法 ,利用锥上不动点指数计算 ,在不要求非线性项 f (x,u)非负的情况下 ,证明 Hammerstein型非线性积分方程 φ(x) =∫Gκ(x,y) f (y,φ(y) ) dy非平凡解和多解存在性的一些新的结果。此结果可用来证明非线性常微分方程两点边值问题解的存在性。 相似文献
6.
显式非线性弥散关系在浅水波变形计算中的应用 总被引：1，自引：0，他引：1
本文参照Ｚｈａｏ和Ａｎａｓｔａｓｉｏｕ的方法,导出了逼近Ｂｏｏｉｊ的非线性弥散关系的近似显式表达式,该式给出的结果与Ｂｏｏｉｊ的非线性弥散关系相当吻合。用中文显式非线性弥散关系,结合会弱非线性效应的缓坡方程,构成含非线性影响项缓坡方程的一个求解浅水波变形问题的方程组。用实验数据对本文模型进行验证,结果表明,显式非线性弥散关系在求解浅水波变形问题时,给出了更符合实验数据的结果。 相似文献
7.
港口中系泊船在波浪作用下运动问题的本质是浅水波浪与浮体的相互作用。与深水情况不同,浅水问题应当考虑水底、水域边界的影响及浅水波浪自身的特性,单一模型很难实现该模拟过程。为此,建立了Boussinesq方程计算入射波和Laplace方程计算散射波的全时域组合计算模型。有限元法求解的Boussinesq方程能使入射波充分考虑到水底、水域边界的影响和浅水波浪的特性;散射波被线性化,采用边界元法求解,并以浮体运动时的物面条件为入射波和散射波求解的匹配条件。该方法为完全的时域方法,计算网格不随时间变动,计算过程较为方便。通过与实验及其他数值方法的结果进行比较,验证了本模型对非线性波面、浮体的运动都有比较理想的计算结果,显示了本模型对非线性问题具有较好的计算能力。 相似文献
8.
本文应用积分方程和时间步进法,考虑了在以流函数理论为基础的非线性规则波作用下,方形墩柱结构上的非线性波浪力和力矩。已有的一些结果表明本文计算值与一些实测结果吻合良好。文章给出了一些可供一般工程设计参考数值计算结果和经验公式。 相似文献
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建立基于四阶完全非线性Boussinesq水波方程的二维波浪传播数值模型。采用Kennedy等提出的涡粘方法模拟波浪破碎。在矩形网格上对控制方程进行离散,采用高精度的数值格式对离散方程进行数值求解。对规则波在具有三维特征地形上的传播过程进行了数值模拟,通过数值模拟结果与实验结果的对比,对所建立的波浪传播模型进行了验证。同时,为了考察非线性对波浪传播的影响,给出和上述模型具有同阶色散性、变浅作用性能但仅具有二阶完全非线性特征的波浪模型的数值结果。通过对比两个模型的数值结果以及实验数据,讨论非线性在波浪传播过程中的作用。研究结果表明,所建立的Boussinesq水波方程在深水范围内不但具有较精确的色散性和变浅作用性能,而且具有四阶完全非线性特征,适合模拟波浪在近岸水域的非线性运动。 相似文献
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Higher order Boussinesq equations 总被引：2，自引：0，他引：2
Z. L. Zou 《Ocean Engineering》1999,26(8):239
A new form of Boussinesq-type equations accurate to the third order are derived in this paper to improve the linear dispersion and nonlinearity characteristics in deeper water. Fourth spatial derivatives in the third order terms of the equations are transformed into second derivatives and present no difficulty in numerical computations. With the increase in accuracy of the equations, the nonlinear and dispersion characteristics of the equations are of one order of magnitude higher accuracy than those of the classical Boussinesq equations. The equations can serve as a fully nonlinear model for shallow water waves. The shoaling property of the equations is also of high accuracy through shallow water to deep water by introducing an extra source term into the second order continuity equation. An approach to increase the accuracy of the nonlinear characteristics of the new equations is introduced. The expression for the vertical distribution of the horizontal velocities is a fourth order polynomial. 相似文献
13.
《Coastal Engineering》2001,44(1):1-12
In order to verify modified mild-slope equation models in a horizontal two-dimensional space, a hydraulic experiment is made for surface wave propagation over a circular shoal on which water depth varies substantially. A horizontal two-dimensional numerical model is also constructed based on the hyperbolic equations that have been developed from the modified mild-slope equation to account for the substantial depth variation. Comparison between experimental measurements and numerical results shows that the modified mild-slope equation model is capable of producing accurate results for wave propagation in a region where water depth varies substantially, while the conventional mild-slope equation model gives large errors as the mild-slope assumption is violated. 相似文献
14.
Numerical modeling of nonlinear resonance of semi-enclosed water bodies: Description and experimental validation 总被引：1，自引：0，他引：1
Inigo J. Losada Jose M. Gonzalez-Ondina Gabriel Diaz-HernandezErnesto M. Gonzalez 《Coastal Engineering》2008
The purpose of this work is to a present a numerical model to solve a set of modified Boussinesq equations to analyse nonlinear resonance of semi-enclosed water bodies. The equations are solved on a finite element unstructured grid in order to achieve an optimal mesh resolution with the local geometry. The model is able to simulate long time lapses and realistic forcing in real bathymetries with a reasonable computational cost. To validate the numerical results, a set of experiments was carried out in a physical model of two adjacent elongated basins. Comparisons between numerical and experimental results for different geometries and nonlinear conditions show that the model is able to simulate with an excellent agreement the transient nonlinear resonant process. 相似文献
15.
实际工程中存在大量的曲边界,因此在曲边界上的计算准确性可以考察出一个数值模型的实用价值。利用Beji的改进型Boussinesq方程建立了一个有限元方法的数值波浪模型。造波方面采用Fenton提出的非线性规则波浪解;在墙边界处,以求解法线方向和切线方向的速度和导数代替求解x、y方向的速度和导数,从而使边界条件直接适用、严格满足,保证了对曲边界计算的准确性。"重开始广义极小残量法"的使用保证了求解方程组的效率和精度,使造波和边界处理方法的有效性和准确性得到了合理地诠释。通过与试验数据、他人数值结果、解析解的比对,显示出该模型计算稳定、结果准确,真正体现出了有限元方法对曲边界适用的优势。 相似文献
16.
A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows 总被引：2，自引：0，他引：2
A set of weakly dispersive Boussinesq-type equations, derived to include viscosity and vorticity terms in a physically consistent manner, is presented in conservative form. The model includes the approximate effects of bottom-induced turbulence, in a depth-integrated sense, as a second-order correction. Associated with this turbulence, vertical and horizontal rotational effects are captured. While the turbulence and horizontal vorticity models are simplified, a model with known physical limitations has been derived that includes the quadratic bottom friction term commonly added in an ad hoc manner to the inviscid equations. An interesting result of this derivation is that one should take care when adding such ad hoc models; it is clear from this exercise that (1) it is not necessary to do so – the terms can be included through a consistent derivation from the viscous primitive equations – and (2) one cannot properly add the quadratic bottom friction term without also adding a number of additional terms in the integrated governing equations. To solve these equations numerically, a highly accurate and stable model is developed. The numerical method uses a fourth-order MUSCL-TVD scheme to solve the leading order (shallow water) terms. For the dispersive terms, a cell averaged finite volume method is implemented. To verify the derived equations and the numerical model, four cases of verifications are given. First, solitary wave propagation is examined as a basic, yet fundamental, test of the models ability to predict dispersive and nonlinear wave propagation with minimal numerical error. Vertical velocity distributions of spatially uniform flows are compared with existing theory to investigate the effects of the newly included horizontal vorticity terms. Other test cases include comparisons with experiments that generate strong vorticity by the change of bottom bathymetry as well as by tidal jets through inlet structures. Very reasonable agreements are observed for the four cases, and the results provide some information as to the importance of dispersion and horizontal vorticity. 相似文献
17.
For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables. 相似文献
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The numerical investigation of random wave slamming on superstructures of marine structures in the splash zone is presented in this paper. The impact pressures on the underside of the structure are computed based on the improved volume of fluid method (VOF). The governing equations are Reynolds time-averaged equations and the two equation k– model. The third order upwind difference scheme is applied to the convection term to reduce the effect of numerical viscosity. The numerical wave flume with random wave-maker suitable for VOF is established. Appropriate moving contact-line boundary conditions are introduced to the model wave in contact with and separated from the underside of structure. Parametric studies have been carried out for different incident waves, structure dimensions and structure clearance. The numerical results are verified by the experimental results. 相似文献
20.
Extended Boussinesq equations for rapidly varying topography 总被引：1，自引：0，他引：1
We developed a new Boussinesq-type model which extends the equations of Madsen and Sørensen [1992. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly varying bathymetry. Coastal Engineering 18, 183-204.] by including both bottom curvature and squared bottom slope terms. Numerical experiments were conducted for wave reflection from the Booij's [1983. A note on the accuracy of the mild-slope equation. Coastal Engineering 7, 191-203] planar slope with different wave frequencies using several types of Boussinesq equations. Madsen and Sørensen's model results are accurate in the whole slopes in shallow waters, but inaccurate in intermediate water depths. Nwogu's [1993. Alternative form of Boussinesq equation for nearshore wave propagation. Journal of Waterway, Port, Coastal and Ocean Engineering 119, 618-638] model results are accurate up to 1:1 (V:H) slope, but significantly inaccurate for steep slopes. The present model results are accurate up to the slope of 1:1, but somewhat inaccurate for very steep slopes. Further, numerical experiments were conducted for wave reflections from a ripple patch and also a Gaussian-shaped trench. For the two cases, the results of Nwogu's model and the present model are accurate, because these models include the bottom curvature term which is important for the cases. However, Madsen and Sørensen's model results are inaccurate, because this model neglects the bottom curvature term. 相似文献