系泊船非线性波浪力时域计算:二维模型

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.     

Generalised synchronisation of spatiotemporal chaos using feedback control method and phase compression

Coupled map lattices are taken as examples to study the synchronisation of spatiotemporal chaotic systems. First, a generalised synchronisation of two coupled map lattices is realised through selecting an appropriate feedback function and appropriate range of feedback parameter. Based on this method we use the phase compression method to extend the range of the parameter. So, we integrate the feedback control method with the phase compression method to implement the generalised synchronisation and obtain an exact range of feedback parameter. This technique is simple to implement in practice. Numerical simulations show the effectiveness and the feasibility of the proposed program.     

Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes

A two-dimensional scour model based on coupled system of shallow water equations (SWEs) and sediment transport on unstructured mesh is developed. The coupled system of hydrodynamic and morphodynamic equations is solved by finite volume method using Godunov scheme. Roe's approximate Riemann solver is used to calculate the inviscid fluxes. The use of unstructured mesh makes the model applicable to complex domains. However, it is difficult to evaluate the eigenvalues and eigenvectors of the Jacobian matrix in the global coordinate. The method proposed herein to deal with this difficulty is to transform the system into the local coordinate with one of the axes in the same direction as the interface outward normal vector. In the local coordinate system, the Jacobian matrix is simplified and the eigenvalues are analyzed using asymptotic method. Regular expansion breaks down when the flow is near critical. Uniformity of the expansion is achieved by changing the scales. Rotational invariance theorem is used to relate the interfacial fluxes in the global and local coordinate systems. Special treatment of the source term on unstructured grid makes the scheme stable and physically balanced (both mass and momentum). The method proposed in this paper for the eigen-system is very efficient comparing to iterative numerical methods. Results from the test cases show good agreement with the experiments.     

非线性波浪时域计算的三维耦合模型

将计算区域Ω划分为内域Ω₁和外域Ω₂(Ω₂=Ω-Ω₁),外域控制方程采用改进线性频散特性的二维Boussinesq方程,用预报一校正法数值求解;结构物附近的内域控制方程为三维Navier-Stokes方程,由VOF方法数值求解。通过在外域和内域相匹配的交界面上设置合适的速度和波面边界条件,建立了三维非线性波浪时域计算的耦合模型。模拟试验表明:(1)耦合模型数值波浪水池可以产生稳定的、重复性较好的波动过程;(2)用耦合模型数值波浪水池求解较大浅水区域上的非线性波浪数值计算问题可以取得较高的计算效率,同时又能得出结构物附近的复杂流场。     

河口海岸泥沙输移的分组数学模型研究

根据河口海岸水沙输移的特点,建立了一个新的二维分组数学模型,用来预测该区域的水沙输移过程。该模型耦合了水动力模块、泥沙输移模块和床面演变模块。其中水动力模块基于浅水方程组,综合考虑了柯氏力、床面切应力以及表面风应力的影响,引入干湿判断法处理动边界。泥沙输移模块首先将泥沙按照粒径分组,针对不同泥砂性质,对各组泥沙分别进行建模求解。床面演变模块基于质量守恒方程,实时更新床面高程以及床沙级配变化,并传递给水动力模块,更新底部边界。该模型被应用在了英国塞汶(Severn)河口,其预测的泥沙浓度和实测数据以及不分组的模型的预测结果进行了比较,结果显示,文中建立的分组模型预测的结果要明显好于不分组模型。     

多波束测深海底数字地形模型的建立

针对多波束测深数据集,采用改进的距离反比权重算法和多细节层次模型技术来建立海底数字地形模型（DTM）。结果表明：本方法具有较高的精度和效率,可以满足不同分辨率要求的DTM应用。     

应用交叉检查数字地形模型评估多波束测深精度

为有效评估多波束测深数据精度,结合Sea Bat 7150深水多波束测量系统在海洋调查工作中的应用实例,参考传统的基于面的交叉检查方法,引入了基于DTM的交叉检查精度评估方法。应用检测线测量数据与主测线DTM进行交叉点计算,对误差进行统计分析,评估多波束测深精度。实践证明,该评估方法快速有效,可操作性强,可在外业调查现场对深水多波束测量数据快速进行精度评估。     

完全非线性波浪与二维固定结构物作用的IGN-BEM耦合分析模型

为高效准确地对完全非线性波浪与二维固定结构物的相互作用进行模拟分析,建立了二维完全非线性时域耦合模型。耦合模型将计算域划分为靠近结构物的内域和远离结构物的外域,每个区域均采用满足完全非线性自由水面边界条件的波浪模型进行求解。在内域使用Laplace方程描述流体运动并采用高阶边界元法（BEM）对其进行求解;而在没有结构物的外域,波浪运动的控制方程为Irrotational Green-Naghdi（IGN）方程并采用有限元法（FEM）对其进行求解。内域和外域通过一段重叠区域进行耦合,从而实现模型间变量的传递。首先利用耦合模型分别对规则波的传播、直墙前立波的生成以及相关物理模型试验进行模拟,数值结果与精确解和试验结果的良好吻合验证了耦合模型耦合方式的合理性以及处理非线性问题的准确性;然后使用耦合模型模拟分析了波浪与固定结构物间的相互作用,并将结果与线性解析解以及完全非线性BEM模型的结果进行了对比分析,进一步证明了耦合模型的正确性与高效性。     

Numerical modelling of liquefaction in loose sand deposits subjected to ocean waves

The failure of marine structures is often attributed to liquefaction in loose sand deposits that are subjected to ocean waves. In this study, a two-dimensional integrated numerical model is developed to characterize the liquefaction behaviours of loosely deposited seabed foundations under various types of ocean waves. In the present model, Reynolds-Averaged Navier–Stokes (RANS) equations are used to simulate the surface wave motion, and Biot's consolidation equations are used to link the solid-pore fluid interactions in a porous medium. A poro-elasto-plastic solution is used to reproduce foundation behaviour under cyclic shearing. Unlike previous investigations, both oscillatory and residual soil responses were considered; they are coupled in an instantaneous approach. Verification of the model results to the previous centrifugal wave tests is carried out, obtaining fairly good agreement. Numerical examples show that foundation behaviour under various types of wave loading, particularly standing waves or a solitary wave, embodies a completely two-dimensional process in terms of residual pore pressure development. The parametric studies demonstrate that liquefaction caused by the build-up of pore pressures is more likely to occur in loosely deposited sand foundations with poor drainage and under large waves.     

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

On the basis of the reproducing kernel particle method (RKPM), a new meshless method, which is called the complex variable reproducing kernel particle method (CVRKPM), for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.     

Dynamic-Stochastic Modeling of Natural Processes

We propose a method for the construction of dynamic-stochastic models of natural systems based on the assimilation of the data of observations in the prognostic equations of coupled processes. In these models, the method of adaptive balance of causes is used to deduce evolutionary equations of the analyzed processes and assimilate the data of observations in these equations. The deduced general equations are considered for an example of a marine ecosystem characterized by the development of four coupled processes. It is shown that the optimal prediction of these processes requires the solution of 11 systems of equations with simultaneous adaptation of prognostic estimates and the coefficients of the models to the data of observations. A numerical simulation experiment explaining the algorithm of the proposed method of modeling is considered. A conclusion is made that the application of this method in the geoinformation systems of monitoring of the environment is quite promising.__________Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 31–42, November–December, 2004.     

On the identification of ship coupled heave–pitch motions using neural networks

This paper outlines a procedure for the derivation of the differential equations describing the free response of a heaving and pitching ship from its stationary response to random waves. The coupled heave–pitch motion of a ship in random seas is modelled as a multi-dimensional Markov process. The partial differential equation describing the transition probability density function, known as the Fokker-Planck equation, for this process is derived. The Fokker-Planck equation is used to derive the random decrement equations for the coupled heave–pitch motion. The parameters in these equations are then identified using a neural network approach. The method is validated using numerical simulations and experimental results. The experimental data was obtained using an icebreaker ship model heaving and pitching in random waves. It is shown that the method produces good results when the system is lightly damped. An extension for using this method to identify couple heave–pitch motion in realistic seas is suggested.     

Numerical simulation for the two-dimensional nonlinear shallow water waves

This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.     

On the identification of ship coupled heave–pitch motions using neural networks

This paper outlines a procedure for the derivation of the differential equations describing the free response of a heaving and pitching ship from its stationary response to random waves. The coupled heave–pitch motion of a ship in random seas is modelled as a multi-dimensional Markov process. The partial differential equation describing the transition probability density function, known as the Fokker-Planck equation, for this process is derived. The Fokker-Planck equation is used to derive the random decrement equations for the coupled heave–pitch motion. The parameters in these equations are then identified using a neural network approach. The method is validated using numerical simulations and experimental results. The experimental data was obtained using an icebreaker ship model heaving and pitching in random waves. It is shown that the method produces good results when the system is lightly damped. An extension for using this method to identify couple heave–pitch motion in realistic seas is suggested.     

二维浅水波方程的间断-连续Galerkin方法

将基于二维简化浅水波模型的间断Galerkin有限元与连续Galerkin有限元耦合方法推广至形式更为复杂的浅水波方程,并给出了误差分析以及模型问题的数值算例。     

面向海底成图基于DTM边界的等值线充填算法

提出一种基于DTM边界线的等值线矢量彩色充填图算法.算法在处理奇异格网点基础上跟踪并存储DTM边界线,通过边界点阵快速建立非封闭等值线与边界线间的双向联系,基于边界线建立非封闭等值线间的拓扑关系并顺序跟踪封闭多边形,通过多边形最小扩展框和转角法(或射线法)建立多边形间的嵌套关系.该算法已成功应用于海量多波束数据成图系统MBChart,解决了常用多波束后处理成图软件栅格充填与等值线之间的失配问题     

求解反应扩散方程的紧致隐积分因子方法

积分因子(IF)方法是近年来提出的求解刚性常微分方程组的一种有效的数值方法。本文应用改进的紧致隐积分因子(cIIF)方法求解二维反应扩散方程。在空间离散上采用二阶中心差分方法。数值模拟得到各种斑图结构与所引文献结果相当一致。     

Simulating offshore sand waves

Sand waves form a prominent regular pattern in the offshore seabeds of sandy shallow seas and pose a threat to a range of offshore activities. A two-dimensional vertical (2DV) flow and morphological simulation model describing the behaviour of these sand waves has been developed. The simulation model contains the 2DV shallow water equations, with a free water surface and a general bed load formula. The water movement is coupled to the sediment transport equation with a seabed evolution equation. The domain is non-periodic in both directions. The spatial discretisation is performed by a spectral method based on Chebyshev polynomials. A fully implicit method is chosen for the discretisation in time. Firstly, we validate the simulation model mathematically by reproducing the results obtained using a linear stability analysis for infinitely small sand waves. Hereby, we investigate a steady current situation induced by a wind stress applied at the sea surface. The bed forms we find have wavelengths in the order of hundreds of metres when the resistance at the seabed is relatively large. The results show that it is possible to model the initial evolution of sand waves with a numerical simulation model. This paper forms the necessary first step to investigate the intermediate term behaviour of sand waves.     

Surface interpolation by a spline technique

A new method for a surface interpolation is proposed, in which the concept of splines under tension is applied. It is useful for the two-dimensional data analysis based on the non-linear fundamental equations in the physical oceanography.     

A NUMERICAL MODEL FOR THE TIDES AND TIDAL CURRENTS IN THE TAIWAN STRAIT

Semidiurnal and diurnal tidal waves in the Taiwan Strait are computed simultaneously by using finite difference method with two-dimensional nonlinear hydrodynamic equations. The agreement between the computed and observed results is considered satisfactory.