Numerical simulation of the internal wave propagation in continuously densitystratified ocean

A numerical model is proposed to simulate the internal wave propagation in a continuously density-stratified ocean, and in the model, the momentum equations are derived from the Euler equations on the basis of the Boussinesq approximation. The governing equations, including the continuity equation and the momentum equations, are discretized with the finite volume method. The advection terms are treated with the total variation diminishing （TVD） scheme, and the SIMPLE algorithm is employed to solve the discretized governing equations. After the modeling test, the suitable TVD scheme is selected. The SIMPLE algorithm is modified to simplify the calculation process, and it is easily made to adapt to the TVD scheme. The Sommerfeld＇s radiation condition combined with a sponge layer is adopted at the outflow boundary. In the water flume with a constant water depth, the numerical results are compared to the analytical solutions with a good agreement. The numerical simulations are carried out for a wave flume with a submerged dike, and the model results are analyzed in detail. The results show that the present numerical model can effectively simulate the propagation of the internal wave.     

平原感潮河网水动力模型研究

利用一维Saint—Venant方程组、河网汊点连续方程及边界条件建立了河网水动力学模型；采用Abbott六点隐式差分格式离散控制方程组；求解河网时，将河段方程自相消元，得到以汊点水位为基本未知量的汊点方程组；采用汊点优化编码来降低汊点方程组系数矩阵的带宽以提高计算精度和节省计算耗时。对上海市平原感潮河网进行了合理概化，利用1999年6月～9月的实测水文资料进行了率定，结果表明计算值同实测值吻合较好。     

二维粘性流动的边界元方法

本文叙述了粘性流动边界元方法，并研究了动力润滑，涡旋发生以及生物力学等问题。该方法基于用Ｓｔｏｌｅｓ方程的基本解作为格林函数，将Ｎ－Ｓ方程归结为求解区域边界上的积分方程，使用边界单元，数值求解积分方程，给出了应力分布、压力分布及速度场。数值结果与理论结果和实验结果十分符合，方法具有很高的精度，比起目前的差分法和有限元法，在某些问题上更有效，也更灵活。     

船闸复杂分散输水系统输水数学模型研究

在推导船闸复杂分散输水系统非恒定流通用的数学模型基本方程的基础上，给出了其在各种输水系统中的应用形式，提出了基本方程求解的全隐差分格式。验证计算结果令人满意。通过数值计算，对出水支孔流量分配规律系统地研究表明，支孔边缘形状、支孔间距和廊道水流损失对支孔流量分配均有影响。     

WAVE-BODY INTERACTIONS FOR A SURFACE-PIERCING BODY IN WATER OF FINITE DEPTH

Nonlinear wave-body interactions for a stationary surface-piercing body in water of finite depth with flat and sloping bottoms are simulated in a two-dimensional numerical wave tank,which is constructed mainly based on the spatially averaged Navier-Stokes equations with the model for simulating the turbulence.The equations are discretized based on the finite volume method and the scheme of the pressure implicit splitting of operators is employed to solve the Navier-Stokes equations.By using the force time h...     

新型高阶Boussinesq水波方程

从经典的Boussinesq方程出发，引入两个参数并对方程中的部分项进行替换，通过严格的数学推导给出量级为O(εμ2)的高阶非线性项，得到一种新型的高阶Boussinesq方程。该方程的色散关系比经典Boussinesq方程提高了一阶，变浅作用性能也得到了改善，方程的适用范围由浅水达到中等水深。利用Crank-Nicloson格式的有限差分法对方程进行数值模型在一维方向上进行离散计算，建立了高阶Boussinesq方程的数值模型。为验证数值模型的正确性，将数值计算结果与Zou等(2001)的物模试验结果以及Beji与Nadaoka方程的数值结果进行对比，本文的数值结果与试验结果吻合程度较好，表明本文方程可适于模拟变水深下的波浪场数值模拟。     

河流水质随机分析模型及其应用

本文以河流ＣＢＯＤ－ＮＢＯＤ－ＤＯ水质方程为例，推导出计算河流水随机分析新模型，该模型将水不质基本方程的各个参数扩展为随机变量，并分解出均值方程一随机脉动量方程，然后求状态变量的积分解和分布矩；其次，利用分布矩和Ｆｏｋｋｅｒ－Ｐｌａｎｃｋ方程产生概述密度函数，模型被应用于清安河的水质模拟，与 ｏｎｔｅＣａｒｌｏ模型和实测资料吻合良好     

基于精细积分法的城市配水系统动态建模

基于功率键合图理论,将所研究的城市配水系统的动态结构绘制成功率键合图,从功率键合图推导出系统的非线性状态空间方程.首先通过增维法将非齐次系统方程转化成齐次方程的形式,避免了系统矩阵求逆,节省计算时间,增强了计算稳定性.模型应用精细积分法迭代求解.实例计算表明,模型计算得到的稳态值同EPANET软件的稳态计算结果一致,验证了算法的正确性.     

含裂隙含水层污染物生物降解数值方法

本文讨论了含裂隙介质地下水污染物输运与生物降解非线性方程组数值求解方法.方程含有对流项、扩散项、生长、死亡、吸附、解吸、趋化和孔隙与裂隙介质界面间的交换项的非线性偶合，使算法十分困难.本文讨论了无生化过程时的几种求解方法，数值结果表明：用三次迎风插值法对常见的对流项占优势，且场变量有较大梯度的问题较适用.在讨论有生化反应过程时，利用对流项与生化反应项的特征时间量级估算，给出了求生化过程作用子步的时间步长估算办法.用上述方法所得到的模拟结果与解析解、无化学反应和有化学反应的实测值对比，吻合很好     

船闸廊道复合管非稳定流的数值计算

在考虑了阀门井水流、各水头损失及廊道和支孔惯性长度的影响之后，推导了船闸廊道复合管非稳定流的基本方程组。阐述了解该方程组的一种数据值迭代方法。计算结果表明，该方程迭代过程稳定、收敛速度较快，且与试验实测值较为吻合。     

Multistage disaggregation processes in stochastic hydrology

The problem of moment preservation associated with the use of the Mejia and Rousselle model in a staged disaggregation scheme is addressed in this paper. General parameter estimation equations are derived. Different from the original parameter estimation equations, the equations proposed herein employ two corrected historical moments which are shown to be conditional on the stage and the annual input generation model. With parameters estimated from the proposed equations, the modeling can exactly preserve the historical moments of interest and maintain the linear relationship between the input and output of each disaggregation process.     

求解大型河网非恒定流的非线性方法

本文以Saint-Venant方程组为基础，用Newton-Raphson方法直接求解按Preiss-mann加权四点隐式格式进行离散所得的非线性代数方程组，提出了河网非恒定流的松弛算法。     

通用一维河网不恒定流软件的研究

本文讨论了通用一维河网不稳定流数值计算软件的数学物理基础：(1)扩展的圣维南方程组及其有限差分方程的牛顿迭代方程组；(2)特殊结点的特殊方程及迭代方程；(3)边界条件和初始条件；(4)系统方程的装配和特殊的高斯消元法.最后用一个例子来与其它的软件进行比较。     

Numerical simulation of flow and bed morphology in the case of dam break floods with vegetation effect

The purpose of this study is to establish a depth-averaged 2-D hydrodynamic and sediment transport model for the dambreak flows with vegetation effect. The generalized shallow water equations are solved using an explicit finite volume method with unstructured quadtree rectangular grid, and in the hydrodynamic model, a Harten-Lax-Van Leer(HLL) approximate Riemann solver is used to calculate the intercell flux for capturing the dry-to-wet moving boundary. The sediment transport and bed variation equations in a coupled fashion are calculated by including the bed variation and the variable flow density in the flow continuity and momentum equations. The drag force of vegetation is modeled as the sink terms in the momentum equations. The developed model is tested against lab experiments of the dam-break flows over a fix bed and a movable bed in vegetated and non-vegetated channels. The results are compared with experimental data, and good agreement is obtained. It is shown that the reduced velocity under vegetated conditions leads to a decrease of the peak discharge and a rise of the water level of rivers and also an enhancement of the sediment deposition.     

明满交替流数值模拟中的精细积分法

建立具有统一形式的明满交替流控制方程。由于系统阵刚性而导致明满交替流数值模拟的计算精度低和收敛性差。在交错网格上对控制方程进行空间上的数值离散后，加入伪时间导数项进行预处理，改善系统阵的刚性。通过采用系统阵增维的方法将非齐次状态空间方程转化为齐次方程，避免了矩阵求逆运算，增强计算的稳定性；预处理后系统方程每一个物理时间步的求解都相当于一个稳态问题，需要花费大量的计算时间，借助于精细积分法可以采用大步长的优势来加快求解速度。有效地解决了明满交替流建模中由于刚性而引起的数值稳定性问题和预处理引起的积分时间较慢的问题。而且这一方法具有程序容易实现的优点。     

THE SLOP FLUX METHOD FOR NUMERICAL BALANCE IN USING ROE＇S APPROXIMATE RIEMANN SOLVER

Imbalance arises when the Roe’s method is directly applied in the shallow water simulation.The reasons are different for the continuity equation and the momentum equations.Based on the Roe’s method,a partial surface method is proposed for a perfect balance for the continuity equation.In order to generate a mathematically hyperbolic formulation,the momentum equations are split,which causes incompatibility in the calculation of the momentum equations.In this article a numerical approach named the Slop Flux Method(SFM)is proposed to balance the source terms and the flux gradient based on the finite volume method.The method is first applied to shallow water equations.The model is verified by analytical results of classical test cases with good agreement.Finally the method is applied to a steady flow simulation over a practical complicated topography and the result shows good balance and conservation.     

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。     

太沙基三维固结方程在一维情况下精确解的物理意义解释

通过建立太沙基一维固结理论体系下位移与孔隙水压力的耦合方程,说明能否体现位移和孔压的耦合关系并不是比奥固结理论优于太沙基固结理论的方面,耦合方程的真正价值在于充当了求解具有更多未知数的比奥固结方程的必要数学条件。相关成果有利于更好地理解固结方程及相关问题的本质,推进固结方程的应用。     

STOCHASTIC ANALYSIS MODEL FOR RIVER WATER QUALITY AND ITS APPLICATION

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复杂输水系统中恒定流的数学模拟

本文提出了一种用于恒定流分析的通用数学模型，该模型把任意复杂的输水系统划分为一些简单的单元，对每个单元建立形式相同的单元方程，将单元方程合成，引入边界条件，就可得到系统的总体方程，然后用节点分组解法求解.该模型具有通用性强、计算速度快、计算精度高等优点，实例分析表明，本文的计算方法是正确的、可行的.