浅水域中多船编队航行时的船波干涉

以Green-Naghdi(GN)方程为基础,采用波动方程和运动网格的有限元法研究多船在浅水域中集体航行时的波浪干涉特性。把运动船舶对水面的扰动作为移动压强直接加在GN方程里,以描述运动船体和水面的相互作用。GN方程合理地考虑非线性和频率散射对浅水船波的影响。以Series60 CB=0.6船体为算例,给出两船并行、前后跟随、三船品字形编队航行时的波浪干涉图形,波浪阻力及侧向力的数值分析结果。计算结果表明:1)当两船并行时,两船承受侧向吸引力,同时波浪阻力稍有增加。2)当两船前后跟随时,两船的波浪阻力都减小。3)当三船品字形航行时,前船的阻力减小,后船的阻力增加,同时后面两船的吸力减小。     

考虑粘性作用情况下船在船厢中运动的水动力学分析

从根据浅水特性在垂直方向所平均化的N-S方程出发,利用有限元计算船舶进出船厢时的水动力学过程和船舶运动过程中的升沉、纵倾及船舶与厢底的最小间隙.由于在平均过程中保留了粘性项,同时产生了底摩擦项,使得到的数学方程更接近真实物理问题,另一方面也增加数值计算的稳定性.本文提出了随非惯性系一起运动的开边界的辐射条件.关于压力的求解,在船底与自由表面分别利用压力泊松方程求压力及自由表面利用连续方程求波高的求解方法.由针对三峡升船机的数值模拟的计算结果看,计算结果合理,计算方法稳定.     

关于采用高阶Boussinesq方程求解波浪散射问题的注记

本文讨论了采用高阶Boussinesq方程模拟波浪散射时对基本速度变量位置的局部光滑处理方法。通过光滑局部基本速度变量的取值深度,减小其高阶导数项的量值、加快级数收敛速度进而改善模型方程求解深水波浪散射问题的能力。对于底部边界具有一阶导数不连续的情况,通过局部光滑．可以将基本速度变量取值深度尖角转化为圆角过渡,从而改善速度分布。对于其它任意变化的底部边界,为了减少高阶底坡导数项的影响,在曲率和高阶底坡导数项与斜率具有相同量级的情况下亦需要对基本速度变量的取值深度局部光滑。数值计算结果表明本文提出的光滑技术可以很好地改善Boussinesq方程模拟浅水波和深水波在斜坡地形上散射问题的能力。     

一个求解浅水波方程的时域分段展开算法

发展了一种时域分段展开自适应方法求解一维非线性浅水波方程。通过时域分段展开,将一个非线性的时空耦合初边值问题转化为一系列的线性空间边值问题,并采用有限元方法递推求解;通过展开阶数的递进,实现了分段时域的自适应计算,当不同步长时可保持稳定的计算精度。研究结果表明,当步长较大而Heun’s法、四阶Runge-Kutta法不能得到合理结果时,本文算法仍能保证足够的计算精度。     

直立码头前船波浪力耦合计算模型

建立了外域用Boussinesq方程、内域用刚体运动方程的直立码头前二维船剖面波浪力的时 域计算耦合模型，内域与外域在交界面的匹配条件是流量连续和压力相等. 进行了相关模型 实验，并把计算结果与实验结果进行了对比. 推导了船体与水底和直立码头之间间隙内流体 运动的自振频率，研究了间隙内流体运动的共振现象.     

考虑惯性效应的渗流方程及相关阻力标度律

本文基于体积平均法推导得到了多孔介质中考虑惯性效应时的局部线化宏观流动方程,由此可以递推得到较大雷诺数Re 时Navier-Stokes 方程的解,从而避免了直接求解Navier-Stokes 方程所带来的计算成本高和计算稳定性差的问题．针对正方形周期排列模型的算例表明,平均速度方向与宏观压力梯度方向并不总是一致,一般情况下,随着Re 增大,二者差异也会增大．当固定平均速度方向v ? 时,压差阻力在较大的Re 范围内存在标度律,标度指数约为3．该标度指数与弱惯性区域标度指数一致,但弱惯性区域Re 范围仅为0相似文献   

再入飞行器湍流尾迹流场研究

再入飞行器湍流尾迹流场状况，直接关系到飞行器的雷达散射特性。对再入飞行器湍流尾迹等离子体场理论模型，试图通过湍流模式理论来表达，即使用κ－ε－g模型方程来封闭平均化的全Navier-Stokes方程，从而准确获得流动平均场和脉动场信息。使用的N－S平均方程由质量加权平均过程产生，湍流模型方也经过可压缩性修正。真实气体效应重点考察空气处于局部热化学平衡状态。流动控制方程运用一个二阶TVD格式的有限体积法求解，以一典型小钝锥体零攻角再入飞行为例，计算了在两种高程（H－40km和H＝30km)条件下的高超声速湍流尾迹流场。获得的尾迹流场参数与流动物理状况符合，并且湍流脉动参数与已有相应的实验结果定性一致，初步证实该方法合理。     

Bingham流体与固壁、液面斜撞击的数值模拟

在交错网格中用MAC方法求解二维不可压N S方程 ,对圆截面液柱与固壁、液面斜撞击问题进行了数值模拟 ,得到了自由面随时间演化的图像。主要考察了 :(1)固壁和液面 ;(2 )牛顿、非牛顿流体 ;(3)碰撞入射角 ;(4 )Bingham流体近似本构式中参数q0 、K对计算结果的影响。结果表明 :液柱与液面碰撞形成的自由面更复杂。碰撞初期 ,Bingham流体和水的自由面相似 ;但碰撞后期 ,Bingham流体的自由面相对简单。对液柱与液面碰撞自由面的影响较大。本文条件下 ,当K 2 0时 ,K对自由面的影响不大 ;当q0 增大时 ,自由面变得相对简单。     

试样尺寸对核电厂主蒸汽管道断裂韧性的影响研究

以某核电厂SA335 材料主蒸汽管道为研究对象,首先结合SA335 的断裂阻力曲线（J-R 曲线）试验测量结果,提出了一种方法确定韧性金属材料裂纹扩展模型（G-T 模型）中的主要微观参数：初始孔隙率0 f 和初始孔隙间距D;随后,在有限元计算中引入G-T 模型模拟了SA335 紧凑拉伸试样的断裂过程,讨论了试样尺寸对于J-R 曲线的影响．结果表明：试样厚度一致时,初始裂纹长度大的试样对应偏低的断裂韧性;当试样尺寸整体缩放时,较大尺寸的试样对应偏低的断裂韧性．最后,结合实例说明了试样整体尺寸对于主蒸汽管道临界裂纹长度的影响．     

纳米压痕过程的三维有限元数值试验研究

采用有限元方法模拟了纳米压痕仪的加、卸载过程，三维有限元模型考虑了纳米压痕仪的标准Berkovich压头．介绍了有限元模型的几何参数、边界条件、材料特性与加载方式，讨论了摩擦、滑动机制、试件模型的大小对计算结果的影响，进行了计算结果与标准试样实验结果的比较，证实了模拟的可靠性．在此基础上，重点研究了压头尖端曲率半径对纳米压痕实验数据的影响．对比分析了尖端曲率半径r＝0与r＝100nm两种压头的材料压痕载荷—位移曲线．结果表明，当压头尖端曲率半径r≠0时，基于经典的均匀连续介质力学本构理论、传统的实验手段与数据处理方法，压痕硬度值会随着压痕深度的减小而升高．     

Extended Mild-Slope Equation

ＩｎｔｒｏｄｕｃｔｉｏｎＡｃｃｕｒａｔｅｍｏｄｅｌｌｉｎｇｏｆｓｕｒｆａｃｅｗａｖｅｄｙｎａｍｉｃｓｉｎｃｏａｓｔａｌｒｅｇｉｏｎｓｈａｓｂｅｅｎｔｈｅｇｏａｌｏｆｍｕｃｈｒｅｃｅｎｔｒｅｓｅａｒｃｈ ,ｗｈｉｃｈｈａｓｂｅｅｎｓｕｍｍａｒｉｚｅｄｉｎｓｕｒｖｅｙｓｂｙＤｉｎｇｅｍａｎｓ( 1 997) [1]ａｎｄＫｉｒｂｙ( 1 997) [2 ].Ｔｈｅｒｉｃｈｎｅｓｓｏｆｃｏａｓｔａｌｗａｖｅｄｙｎａｍｉｃｓａｒｉｓｅｓｆｒｏｍｔｈｅｓｔｒｏｎｇａｍｂｉｅｎｔｃｕｒｒｅｎｔｓａｎｄｔｈｅｗｉｄｅｖａｒｉａｔｉｏｎｓ…     

Numerical computations of two-dimensional solitary waves generated by moving disturbances

Two-dimensional solitary waves generated by disturbances moving near the critical speed in shallow water are computed by a time-stepping procedure combined with a desingularized boundary integral method for irrotational flow. The fully non-linear kinematic and dynamic free-surface boundary conditions and the exact rigid body surface condition are employed. Three types of moving disturbances are considered: a pressure on the free surface, a change in bottom topography and a submerged cylinder. The results for the free surface pressure are compared to the results computed using a lower-dimensional model, i.e. the forced Korteweg–de Vries (fKdV) equation. The fully non-linear model predicts the upstream runaway solitons for all three types of disturbances moving near the critical speed. The predictions agree with those by the fKdV equation for a weak pressure disturbance. For a strong disturbance, the fully non-linear model predicts larger solitons than the fKdV equation. The fully non-linear calculations show that a free surface pressure generates significantly larger waves than that for a bottom bump with an identical non-dimensional forcing function in the fKdV equation. These waves can be very steep and break either upstream or downstream of the disturbance.     

Linear gravity waves on Maxwell fluids of finite depth

Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper. A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived. A dimensionless memory (time) number 0 is introduced. The dispersion equation for the pure viscous fluid will be a specific case of the dispersion equation for the viscoelastic fluid as θ=0. The complex dispersion equation is numerically solved to investigate the dispersion relation. The influences of θ and water depth on the dispersion characteristics and wave decay are discussed. It is found that the role of elasticity for the Maxwell fluid is to make the surface gravity wave on the Maxwell fluid behave more like the surface gravity wave on the inviscid fluid.     

A finite element method for two‐dimensional water‐wave problems

In this paper, the authors treat the free‐surface waves generated by a moving disturbance with a constant speed in water of finite and constant depth. Specifically, the case when the disturbance is moving with the critical speed is investigated. The water is assumed inviscid and its motion irrotational. The surface tension is neglected. It is well‐known that the linear theory breaks down when a disturbance is moving with the critical speed. As a remedy to overcome the invalid linear theory, approximate non‐linear theories have been applied with success in the past, i.e. Boussinesq and Korteweg de Vries equations, for example. In the present paper, the authors describe a finite element method applied to the non‐linear water‐wave problems in two dimensions. The present numerical method solves the exact non‐linear formulation in the scope of potential theory without any additional assumptions on the magnitude of the disturbances. The present numerical results are compared with those obtained by other approximate non‐linear theories. Also presented are the discussions on the validity of the existing approximate theories applied to two types of the disturbances, i.e. the bottom bump and the pressure patch on the free‐surface at the critical speed. Copyright © 1999 John Wiley & Sons, Ltd.     

On time-dependent,two-layer flow over topography: II. Evolution and propagation of solitary waves

The evolution of topographically generated interfacial motion is considered in a two-layer model. A system of two non-linear equations, similar to the Boussinesq equations for shallow water waves, is derived. The consequences of the cubic non-linearity of these equations on the nature of the solitary wave solutions are explored. A dispersion relation for solitary waves implies the existence of maxima for speed and displacement in a wave. The limiting values are shown to agree with other studies. The growth of solitary and/or cnoidal waves is studied for finite pulses of displacement and for internal bores.     

时域Rankine源法求解有限水深船舶在规则波中的水底压力变化

应用势流理论中的Rankine源面元法和时域步进法,求解了有限水深船舶在规则波中运动的水底压力变化。将速度势分解成基本势、局部势和记忆势,以叠模解作为基本势对自由表面条件和物面条件进行了线性化,通过在水底布置面元来满足水底条件。利用研制的水底压力-水面波浪测量系统,测量了不同入射波船模表面波形与水底压力的时历曲线,理论计算与实验结果符合较好,验证了自编程序的正确性。通过对比二者的等高线图发现,水底压力与表面波形的峰谷有较好的一致性,并且压力较波形更为平滑。     

NUMERICAL SIMULATION OF SHALLOW WATER WAVE PROPAGATION USING A BOUNDARY ELEMENT WAVE EQUATION MODEL

The present paper makes use of a wave equation formulation of the primitive shallow water equations to simulate one-dimensional free surface flow. A numerical formulation of the boundary element method is then developed to solve the wave continuity equation using a time-dependent fundamental solution, while an explicit finite difference scheme is used to derive velocities from the primitive momentum equation. One-dimensional free surface flows in open channels are treated and the results compared with analytical and numerical solutions. © 1997 John Wiley & Sons, Ltd.     

Boussinesq方程的发展形式与Airy波理论差异性研究

应用势流理论，采用递推函数方法推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程。通过对新方程的参数设置，可以讨论出Ｂｏｕｓｓｉｎｅｓｑ方程发展趋势和不同的发展形式。对浅水波动的描述方程，Ｂｏｕｓｓｉｎｅｓｑ方程的发展趋势为适用水深范围的拓展。拓展应用范围的大小则由其方程频散特征向Ａｉｒｙ波频散解逼近程度来决定。而Ｂｏｕｓｉｎｅｑ方程又不同于Ａｉｒｙ波，主要原因是Ｂｏｕｓｓｉｎｅｓｑ方程中含有线性频散项，Ａｉｒｙ波则只是长波首项近似，无线性频散项。其频散特征为精确的线性频散解。对实际水波传播而言，Ａｉｒｙ波理论的局限性是不言而喻的。     

A numerical method for the determination of weakly non‐hydrostatic non‐linear free surface wave propagation

A numerical method is described that may be used to determine the propagation characteristics of weakly non‐hydrostatic non‐linear free surface waves over a general, bottom topography. In shallow water of constant undisturbed depth, such waves are equivalent to the familiar cnoidal waves characterized by sharp crests and relatively flat troughs. For a certain range of parameters, these propagate without change of form by virtue of the weakly non‐hydrostatic balance in the vertical momentum equation. Effectively, this counters the tendency for the non‐linearity in a purely hydrostatic theory to lead to a continuously deforming surface wave profile. The realistic representation furnished by cnoidal wave theory of free surface waves in the shallow near‐shore zone has led to its utilization in evaluating their propagation characteristics. Nonetheless, the classic analytical theory is inapplicable to the case of wave propagation over a sloping beach or off‐shore sand bar topography. Under these conditions, a local change in form of the surface wave profile is anticipated before the waves break and knowing this is required in order to evaluate fully the propagation process. The efficacy of the numerical method is first demonstrated by comparing the solution for water of constant depth with the evaluation of the analytical solution expressed in terms of the Jacobian elliptic function cn. The general method described in the paper is then illustrated by experiments to determine the change in profile of weakly non‐hydrostatic non‐linear surface waves propagating over bed forms representative of those found in shallow coastal seas. Copyright © 2001 John Wiley & Sons, Ltd.