THE OPTIMAL MOTION OF TWO-DIMENSIONAL UNDULATING PLATE SWIMMING IN FLUID FLOW

The optimum shape of a two-dimensional undulatory plate in its motion in fluid flow is analyzed and the physical parameters(the thrust and the power)are calculated by the boundary element method.With the commonly used Lagrange multiplier method,only a saddle point of the optimum solution can be obtained,but not the solution itself due to the singularity of the problem.To eliminate the singularity,a method is proposed by adding an amplitude constraint.The new method is a generalization of that proposed by Wu,and it can be applied to more complex cases.The optimum shape of the linearly varying amplitude motion is studied in detail.It is shown that both the maximum and the minimum solutions exist when the frequency is higher than a critical value.For a high frequency,the maximum efficient motion with a large amplitude at the leading edge and a small amplitude at the trailing edge induces a large leading edge suction force.As the frequency decreases,the leading edge suction force decreases to a minimum and then increases.For high wavenumbers,there exists an optimum frequency with the maximum efficiency.High efficiency holds over a large range of frequency.The optimum efficiency increases as the wavenumber increases.The increase of the wavenumber can also reduce the leading edge suction force.The optimization method can also be applied to a quadratically varying amplitude motion.It is found that the optimum efficiency is larger than that for the linearly varying amplitude motion.However,the additional efficiency is relatively small,especially as the original efficiency is already high enough.     

Risk analysis of slope instability of levees under river sand mining conditions

Levees are affected by over-exploitation of river sand and river adjustments after the formation of sand pits. The slope stability is seriously threatened, drawing wide concern among experts and scholars in the area of water conservancy. This study analyzed the uncertainties of slope stability of levees under river sand mining conditions, including uncertainty caused by interest- driven over-exploitation by sand mining contractors, and uncertainty of the distance from the slope or sand pit to the bottom of the levee under the action of cross-flow force after the sand pit forms. Based on the results of uncertainty analysis, the distribution and related parameters of these uncertainties were estimated according to the Yangtze River sand mining practice. A risk model of the slope instability of a levee under river sand mining conditions was built, and the possibility of slope instability under different slope gradients in a certain reach of the Yangtze River was calculated with the Monte Carlo method and probability combination method. The results indicated that the probability of instability risk rose from 2.38% to 4.74% as the pits came into being.     

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.     

Water flooding optimization with adjoint model under control constraints简

The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil production at a minimum cost, and represents the future direction of oil fields. This paper discusses the core of the smart field theory, mainly the real-time optimization method of the injection-production rate of water-oil wells in a complex oil-gas filtration system. Computing speed is considered as the primary prerequisite because this research depends very much on reservoir numerical simulations and each simulation may take several hours or even days. An adjoint gradient method of the maximum theory is chosen for the solution of the optimal control variables. Conven-tional solving method of the maximum principle requires two solutions of time series： the forward reservoir simulation and the backward adjoint gradient calculation. In this paper, the two processes are combined together and a fully implicit reservoir simulator is developed. The matrixes of the adjoint equation are directly obtained from the fully implicit reservoir simulation, which accelera-tes the optimization solution and enhances the efficiency of the solving model. Meanwhile, a gradient projection algorithm combined with the maximum theory is used to constrain the parameters in the oil field development, which make it possible for the method to be applied to the water flooding optimization in a real oil field. The above theory is tested in several reservoir cases and it is shown that a better development effect of the oil field can be achieved.     

A 2-D HYDRODYNAMIC MODEL FOR THE RIVER, LAKE AND NETWORK SYSTEM IN THE JINGJIANG REACH ON THE UNSTRUCTURED QUADRANGLES

The main river,the Dongting Lake and river networks in the Jingjiang reach of the Yangtze River constitute a complex water system,for which a full 2-D hydrodynamic model is established instead of the traditional 1-D or compound models for simulation of such complex systems,based on the latest developments of computer technologies and numerical methods.To better handle irregular boundaries and keep the computation cost well in a reasonable limit,unstructured grids of moderate scale are used. In addition,a dynamic boundary tracking method is proposed to simulate variable flow domains at different floods,especially,when the moderate scale gird can not describe flows in narrow river-network channels at low water levels.Theθsemi-implicit method and the Eulerian-Lagrangian Method(ELM)are adopted,which make the model unconditionally stable with respect to the gravity wave speed and Courant number restrictions.Properties and efficiency of the model are discussed,and it is concluded that the new model is robust and efficient enough for the simulation of a big,complex water system.Validation tests show that the simulation results agree well with field data.It takes about 0.96 h to complete the computation of a 76 d flood,which indicates that the model is efficient enough for engineering applications.     

NUMERICAL SIMULATION OF WAVE RESISTANCE OF TRIMARANS BY NONLINEAR WAVE MAKING THEORY WITH SINKING AND TRIM BEING TAKEN INTO ACCOUNT

Up to now, there are no satisfactory numerical methods for simulating wave resistance of trimarans, mainly due to the difficulty related with the strong nonlinear features of the piece hull wave making and their interference. This article proposes a numerical method for quick and effective calculation of wave resistance of trimarans to be used in engineering applications. Based on Wyatt’s work, the nonlinear free surface boundary condition, the time domain concept, and the full nonlinear wave making theory, using the Rankine source Green function, the 3-D surface panel method is expanded to solve the trimaran wave making problems, with high order nonlinear factors being taken into account, such as the influence of the sinking and trim, transom, and ship wave immersed hull surface. And the software is successfully developed to implement the method, which is validated. Several trimaran models, including a practical trimaran with a sonar dome and the transom, are used as numerical calculation samples, their wave making resistance is calculated both by the present method and some other methods such as linear (Dawson) methods. Moreover, sample model resistance tests were carried out to provide data for comparison, validation and analysis. Through the validation by model experiments, it is concluded that present method can well predict the wave making resistance, sinking and trim, and the accuracy of wave making resistance calculation is significantly improved by taking the trim and sinking into account, especially at high speeds.     

Fuzzy stochastic generalized reliability studies on embankment systems based on first-order approximation theorem

In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.     

Flood risk control of dams and dykes in middle reach of Huaihe River简

Three stochastic mathematical models for calculation of the reservoir flood regulation process, river course flood release, and flood risk rate under flood control were established based on the theory of stochastic differential equations and features of flood control systems in the middle reach of the Huaihe River from Xixian to the Bengbu floodgate, comprehensively considering uncertain factors of hydrology, hydraulics, and engineering control. They were used to calculate the flood risk rate with flood regulation of five key reservoirs, including the Meishan, Xianghongdian, Nianyushan, Mozitan, and Foziling reservoirs in the middle reach of the Huaihe River under different flood frequencies, the flood risk rate with river course flood release under design and check floods for the trunk of the Huaihe River in conjunction with relevant flood storage areas, and the flood risk rate with operation of the Linhuaigang Project under design and check floods. The calculated results show that （l） the five reservoirs can withstand design floods, but the Xianghongdian and Foziling reservoirs will suffer overtopping accidents under check floods; （2） considering the service of flood storage areas under the design flood conditions of the Huaihe River, the mean flood risk rate with flood regulation of dykes and dams from Xixian to the Bengbu floodgate is about 0.2, and the trunk of the Huaihe River can generally withstand design floods; and （3） under a check flood with the flood return period of 1 000 years, the risk rate of overtopping accidents of the Linhuaigang Project is not larger than 0.15, indicating that it has a high flood regulation capacity. Through regulation and application of the flood control system of the Linhuigang Project, the Huaihe River Basin can withstand large floods, and the safety of the protected area can be ensured.     

Numerical simulation of shallow-water flooding using a two-dimensional finite volume model

A 2-D Finite Volume Model (FVM) is developed for shallow water flows over a complex topography with wetting and drying processes. The numerical fluxes are computed using the Harten, Lax, and van Leer (HLL) approximate Riemann solver. Second-order accuracy is achieved by employing the MUSCL reconstruction method with a slope limiter in space and an explicit two-stage Runge-Kutta method for time integration. A simple and efficient method is introduced to deal with the wetting and drying processes without any correction of the numerical flux term or the source term. In this new method, a switch of alternative schemes is used to compute the water depths at the cell interface to obtain the numerical flux. The model is verified against benchmark tests with analytical solutions and laboratory experimental data. The numerical results show that the model can simulate different types of flood waves from the ideal flood wave to cases over complex terrains. The satisfactory performance indicates an extensive application prospect of the present model in view of its simplicity and effectiveness.     

NUMERICAL STUDIES FOR GAS SOLID TWO PHASE STEADY MIXED CONVECTION PROBLEMS WITH PHASE CHANGE

A mathematical model for describing gas solid two phase steady mixed convection with phase change has beendeveloped and numerical calculation methods presented.A melting liquid droplet failing a counter gas currenl expe-riences three processes,cooling of liquid droplet,solidification and cooling of the solid particle.The turbulent modelused for Rayleigh number greater than 10~6 is a two equation(k—ε)model of turbulence.For phase change,animproved enthalpy method with varied time step is proposed.The gas particle two phase flow is described by usingEulerian-Lagrangian approach.Modified SIMPLE algorithm and Runge-Kutta method are used in interative calcu-lation.As an example of calculation,the flow in a special 2-dimensional axi-symmetrical prilling tower of diameter20 m and height 50 m has been performed.Buoyancy effect is important for moving droplet with phase change.The model to be developed and analysis of results obtained in this paper are useful for engineering design in indus-try.     

模拟最大熵法及其在水库泄洪风险计算中的应用

快速简便的风险计算方法是大型复杂工程系统风险分析的重要前提。基于随机模拟和最大熵方法的优点，提出了风险计算的模拟最大熵法（SMEM），并建立了相应的数学模型；将该方法应用于水库工程的泄洪风险计算，并对其计算结果进行了验证、分析和比较。结果表明，在信息相同的条件下，此方法不但可以充分利用已知条件，得到待求的概率分布及风险值，而且在计算速度上也比随机模拟方法（Monte-Carlo）快20多倍，大大提高了计算速度，为风险的计算提供了一个新的思路。     

随机观测误差对水环境评价的影响

水环境评价既存在模糊性，又不可避免随机性。以往评价大多只考虑了实测指标的物理权重的影响，而很少考虑指标实测过程中不可避免的随机观测误差的影响。本文先应用了最大熵原理来确定在给定约束条件(即已知信息)下，实测指标最小偏差的先验概率分布。在此基础上，应用蒙特卡罗法构造算例，进一步讨论了单一模糊模型和基于最大熵原理的相对隶属度模糊优化评价模型Ⅰ与Ⅱ，分为方差不均一和方差均一两种情况，分别研究了随机观测误差对上述水环境评价模型的影响。结果表明：随机观测误差对水环境评价的影响不容忽视，有时甚至直接改变评价等级；当观测精度有差异，尤其差异较大时，这种影响也随之加大，此时，评价结果只取决于某一(几)项随机观测误差最小的指标。     

用蒙特卡罗法解堰闸流动

本文首次运用不规则游动网格的蒙特卡罗方法求解堰闸流动问题.根据蒙特卡罗方法可以独立计算区域内任一点值的特点，提出了相应的自由表面和流量的迭代计算方法.经过多组计算表明，本文方法灵活、快速，流量系数、堰面压力分布的计算值与试验值吻合良好，为蒙特卡罗法求解有自由表面的流动问题取得了成功的经验。     

水工钢闸门主梁模糊失效概率计算方法研究

为合理计算水工钢闸门主梁模糊失效概率,分别将主梁相对变形当作一个随机变量及三个变量的组合,采用积分法、当量随机化方法及蒙特卡罗法进行了计算。当相对变形为一个随机量时,采用积分法及当量随机化方法计算,两者的差别在于积分法用隶属函数描述模糊限值,当量随机化方法是将模糊限值当量作为一个随机量。当相对变形看作三个变量的组合时采用蒙特卡罗法进行计算,该方法考虑了三个变量的分布特性,更符合实际情况,模糊限值也用随机量表示。计算表明,积分法与当量随机化方法结果相近,验证了当量随机化方法的精度;蒙特卡罗法结果与相对变形服从正态分布时、用当量随机化方法计算的结果接近,故主梁相对变形服从正态分布更为合理。三种计算方法中,当量随机化方法计算失效概率相较于其它方法有计算过程简便,效率高的优点。     

Monte-Carlo方法求解水动力学方程的原理及实践

介绍Monte Carlo方法的基本思想及求解Poisson方程的原理 ;利用Monte Carlo方法及图论建立河网计算的随机游动模型 ,并应用于实际的大型河网中 ,取得了较好的结果 .利用Monte Carlo方法计算河网可以避免解大型的稀疏矩阵 ,计算简单、灵活     

Parameter estimations for 2-parameter Pareto distribution by pome

The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 2-parameter Pareto distribution. Monte Carlo simulated data were used to evaluate this method and compare it with the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). The parameter estimates yielded by POME were either superior or comparable for small sample sizes when bias and RMSE were used as the criteria, and were either comparable or adequate for large sample sizes.     

Stochastic simulation of fluid flow in porous media by the complex variable expression method

A stochastic simulation of fluid flow in porous media using a complex variable expression method (SFCM) is presented in this paper. Hydraulic conductivity is considered as a random variable and is then expressed in complex variable form, the real part of which is a deterministic value and the imaginary part is a variable value. The stochastic seepage flow is simulated with the SFCM and is compared with the results calculated with the Monte Carlo stochastic finite element method. In using the Monte Carlo method to simulate the stochastic seepage flow field, the hydraulic conductivity is assumed in three different probability distributions using random sampling method. The obtained seepage flow field is examined through skewness analysis, and the skewed distribution probability density function is given. The head mode value and the head comprehensive standard deviation are used to represent the statistics of calculation results obtained by the Monte Carlo method. The stochastic seepage flow field simulated by the SFCM is confirmed to be similar to that given by the Monte Carlo method from numerical aspects. The range of coefficient of variation of hydraulic conductivity in SFCM is larger than used previously in stochastic seepage flow field simulations, and the computation time is short. The results proved that the SFCM is a convenient calculating method for solving the complex problems.     

考虑参数空间变异性的盾构隧道施工地层变形综合可靠度分析

依托厦门地区典型风化花岗岩地层的盾构隧道工程,针对多层土双线盾构隧道施工地层变形问题,以岩土体参数的空间变异性为切入点,基于随机场理论,采用蒙特卡洛法与有限差分法模拟计算相结合的方法,开展盾构隧道施工地层变形响应的可靠度分析。以土体弹性模量E的空间变异性为研究重点,系统研究土体弹性模量的竖向、水平波动距离(θ_z,θ_x)对地层变形可靠度指标的影响。结果表明:随机分析所得最大地层变形(地表沉降、拱顶沉降、围岩收敛)的可靠度指标随着土体弹性模量波动距离的增大而降低;随着最大地层变形允许值的增大,地层变形可靠度指标也相应提高。在此基础上,借助熵理论客观确定各地层变形指标(地表沉降、拱顶沉降、围岩收敛)的权重系数,结合可靠度设计方法和工程风险分析理论,开展地层变形综合可靠度分析及控制指标体系的研究,提出适合厦门地区的盾构隧道施工地层变形控制指标体系。     

有限差分强度折减法中融合蒙特卡洛思想的边坡可靠性分析

可靠性分析是边坡工程研究的热点之一,但目前基于强度折减方法的边坡可靠度分析研究较少,文章主要是在有限差分强度折减法基础上融合蒙特卡洛思想进行边坡可靠性分析.其研究思路为:首先详细概述了边坡可靠性分析原理及边坡可靠度分析统计模型;其次,介绍了有限差分强度折减法及蒙特卡洛思想,并将蒙特卡洛思想引入边坡有限差分强度折减模型,...     

蒙特卡洛随机模拟法在水电工程风险分析中的应用

蒙特卡洛随机模拟法是水电工程经济评价风险分析中的一种重要方法，本文以实例介绍了此方法在水电工程的具林应用，并取得了较好的效果。