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构造1种光滑的分片Lagrange型插值多项式空间,并在此空间中利用Galerkin法对非线性Klein-Gordon(NKG)方程进行求解.并分析数值格式的稳定性和收敛性,进行数值实验.数值结果表明格式精确有效. 相似文献
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本文给出三角形单元集中质量有限元解浅水波方程的方法以及该方法在IBM-PC微机上的应用实例并取得较好结果。 相似文献
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浅水环境中，多次波广泛发育且很难压制。与一次有效波相比，多次波具有反射角小、传播路径长、照明范围广等优点，如何较好地处理浅水自由表面多次波是海洋地震资料处理的重要环节。本文改变将多次波当作噪音进行压制的做法，实现对其有效利用。首先基于确定性水层多次波压制（DWD）技术加自由表面多次波压制（SRME）技术联合实现对于浅水自由表面多次波与有效反射波的良好分离；然后利用分离的有效波通过反馈环理论实现不同阶次多次波的预测；最后基于成像精度更高的逆时偏移成像技术，实现不同阶次多次波的分阶成像。模型资料和实际资料的试处理结果表明，组合分离方法实现了对浅水自由表面多次波与反射波的良好分离，而分阶成像既避免了成像过程中串扰噪音的影响，又通过利用不同阶次多次波进行成像，扩大了成像照明范围，提升了浅水发育区域地震资料的成像质量，实现了对浅水自由表面多次波的有效利用。 相似文献
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非线性效应对浅水水波变形的影响 总被引：3，自引：0，他引：3
本文采用波数矢量无旋和波能守恒方程建立了一个考虑非线性作用的浅水水波变形数值模型,模型中采用Ｂａｔｔｊｅｓ关系与波数矢量无旋,波能守恒方程一起来求解波浪在浅水中变形的波浪要素,在波能守恒方程中考虑了底摩擦的影响。利用本文提出的数值模型对一个斜坡浅滩水域波浪折射绕射现象进行了验证,验证计算中用一个非线性经验弥散关系近似浅水水波变形的非线性效应并与用线性弥散关系的计算结果进行了比较,结果说明使用非线性 相似文献
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采用受控的自回归滑动平均模型(CARMA)分别研究了珠江河口洪、枯季对外海潮波响应的固有频率。枯季采用单输入单输出模型,洪季采用双输入单输出模型,通过验证、检验表明,模型(CARMA)可用于寻求复杂网河对外海潮波响应的固有频率,方法可靠,易操作。通过频率增益响应分析,发现枯季珠江河口的固有频率以浅水分潮频段为主,对应周期介于6~10.0 h之间,枯季固有频率未出现在全日潮波对应的频段。洪季珠江河口的固有频率也以浅水分潮频段为主,珠江河口对浅水分潮的系统增益响应幅值最大。固有频率接近浅水分潮频段的站点,枯季较洪季固有频率减小,对应周期延长。 相似文献
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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
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浅水地震勘探中，由于水层较浅，多次波普遍发育，而且很难压制，如何更好地压制浅水多次波成为了海洋地震资料处理的重要环节。目前来说，依靠单一的多次波压制技术很难将浅水多次波压制彻底，因此本文探索了一种组合压制浅水多次波的思路，首先基于确定性水层多次波压制方法（DWD）将短周期多次波实现压制，然后采用自由表面多次波压制技术（SRME）将近偏移距长周期多次波进行压制，最后再采用高精度Radon变换，将残留的中、远偏移距长周期多次波完成压制。通过辽东湾海域浅水实际资料的多次波压制效果可以看出，组合压制技术实现了对于资料中发育的浅水多次波的良好压制，陷波频率得到较好的恢复，资料品质得到有效改善，信噪比得到有效提高。 相似文献
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A new set of equations of motion for wave propagation in water with varying depth is derived in this study. The equations expressed by the velocity potentials and the wave surface elevations include first-order non-linearity of waves and have the same dispersion characteristic to the extended Boussinesq equations. Compared to the extended Boussinesq equations, the equations have only two unknown scalars and do not contain spatial derivatives with an order higher than 2. The wave equations are solved by a finite element method. Fourth-order predictor–corrector method is applied in the time integration and a damping layer is applied at the open boundary for absorbing the outgoing waves. The model is applied to several examples of wave propagation in variable water depth. The computational results are compared with experimental data and other numerical results available in literature. The comparison demonstrates that the new form of the equations is capable of calculating wave transformation from relative deep water to shallow water. 相似文献
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针对目前缓坡方程中势函数假设比较多的问题,本文利用二维浅水方程来描述海浪水质点运动的有势假设,采取WKBJ方法推导缓坡方程在缓变地形下的波包方程,对势函数缓坡方程进行修正,以建立更全面更实用的近岸波浪传播计算模式。同时,文中还采用非势函数型模拟波浪传播。 相似文献
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一种基于Roe格式的有限体积法在二维溃坝问题中的应用 总被引：3，自引：0，他引：3
溃坝属于典型的非恒定含间断的浅水问题。应用有限体积法离散二维浅水控制方程的守恒型方程组,将基于近似黎曼解的Roe格式用于数值计算溃坝问题,并利用MUSCL方法构造二阶空间积分格式和预测-校正二步法构造二阶时间格式,从而使数值解的整体达到二阶,提高了精度。文中算法在一维溃坝的Stoker问题的数值结果与解析解进行对比,结果证明了此方法的可行性。应用此方法在二维溃坝问题上的结果,说明了此算法可有效模拟溃坝水流的演进过程。 相似文献
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根据湍流封闭理论,建立一种适用于正压浅海湍流运动的雷诺应力封闭模型(RSM),以代替目前三维浅海动力学模型中普遍采用的湍粘性系数的传统假设。通过直接建立并模化f—平面上正压海洋的雷诺应力传输方程,分别得到的微分形式和代数形式的RSM方程组。并讨论了进行数值计算所需要的边界条件。利用该模型可以进一步研究浅海潮流、风暴潮流及风海流等浅海流动的三维结构和湍流特性。 相似文献
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《Coastal Engineering》2004,51(1):1-15
The shallow water equations (SWE) have been used to model a series of experiments examining violent wave overtopping of a near-vertical sloping structure with impacting wave conditions. A finite volume scheme was used to solve the shallow water equations. A monotonic reconstruction method was applied to eliminate spurious oscillations and ensure proper treatment of bed slope terms. Both the numerical results and physical observations of the water surface closely followed the relevant Rayleigh probability distributions. However, the numerical model overestimated the wave heights and suffered from the lack of dispersion within the shallow water equations. Comparisons made on dimensionless parameters for the overtopping discharge and percentage of waves overtopping between the numerical model and the experimental observations indicated that for the lesser impacting waves, the shallow water equations perform satisfactorily and provide a good alternative to computationally more expensive methods. 相似文献
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Based on Green–Naghdi equation this work studies unsteady ship waves in shallow water of varying depth. A moving ship is regarded as a moving pressure disturbance on free surface. The moving pressure is incorporated into the Green–Naghdi equation to formulate forcing of ship waves in shallow water. The frequency dispersion term of the Green–Naghdi equation accounts for the effects of finite water depth on ship waves. A wave equation model and the finite element method (WE/FEM) are adopted to solve the Green–Naghdi equation. The numerical examples of a Series 60 (CB=0.6) ship moving in shallow water are presented. Three-dimensional ship wave profiles and wave resistance are given when the ship moves in shallow water with a bed bump (or a trench). The numerical results indicate that the wave resistance increases first, then decreases, and finally returns to normal value as the ship passes a bed bump. A comparison between the numerical results predicted by the Green–Naghdi equation and the shallow water equations is made. It is found that the wave resistance predicted by the Green–Naghdi equation is larger than that predicted by the shallow water equations in subcritical flow
, and the Green–Naghdi equation and the shallow water equations predict almost the same wave resistance when
, the frequency dispersion can be neglected in supercritical flows. 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
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We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with which elemental assembly and mass averaging are applied in the forward and in the adjoint systems. Our derivation can be extended to obtain an adjoint for any Galerkin finite element and spectral element system.We begin the derivations using a linear wave equation in one dimension. We then apply our technique to a two-dimensional shallow water ocean model and test it on a classic double-gyre problem. The spectral element forward and adjoint ocean models can be used in a variety of inverse applications, ranging from traditional data assimilation and parameter estimation, to the less traditional model sensitivity and stability analyses, and ensemble prediction. Here the Euler–Lagrange equations are solved by an indirect representer algorithm. 相似文献