基于降雨空间变异的潜水运动随机模拟方法Ⅰ——非条件模拟

将降雨视为随机场,考虑降雨入渗补给量与地下水埋深的关系,采用二维稳定-非稳定潜水运动的KLPC模型,分析了降雨的空间变异性对水头均值、方差和协方差的影响,利用变异系数描述了水头、流速和水动力弥散系数的变异程度。结果表明,KLPC算法的随机模型具有优越的计算效率;水头方差随降雨场方差和相关长度的增大而增大;在降雨空间变异的条件下,水头随机场呈现出明显的非平稳特性且具有各向异性结构;在非稳定流中,水头协方差表现出“扩散”和“平移”的特性;水头的变异程度较小,在随机模拟中可以不考虑降雨空间变异对地下水流动的影响;但水头的变异导致了流速和水动力弥散系数强烈的变异性,在溶质运移的随机分析中需要予以充分重视。     

基于van Genuchten-Mualem模型的饱和-非饱和介质流动随机数值分析

基于van Genuchten-Mualem非饱和水分特征模型，联合运用Karhunen-Loeve展开法、混沌多项式展开以及摄动方法，对饱和-非饱和流问题进行随机数值分析。将土壤特性参数假定为协方差已知的随机函数，并按Karhunen-Loeve法分解，把压力水头表示为多项式。通过摄动方法得到一系列关于水头展开式的偏微分方程，用有限差分法进行求解，获得了压力水头的随机描述，并计算其均值和方差。应用本文的随机模型研究了二维非饱和以及饱和-非饱和介质流动的实例，结果与动量方法的计算结果一致，而且计算效率高于传统的动量方法。     

STOCHASTIC ANALYSIS OF WATER FLOW IN HETEROGENEOUS MEDIA

A stochastic model for saturated-unsaturated flow is developed based on the combination of the KarhunenLoeve expansion of the input random soil properties with a perturbation method. The saturated hydraulic conductivity ks(x) is assumed to be log-normal random functions, expressed by f(x). f(x) is decomposed as infinite series in a set of orthogonal normal random variables by the Karhunen-Loeve (KL) expansion and the pressure head is expand as polynomial chaos with the same set of orthogonal random variables. With these expansions, the stochastic saturated-unsaturated flow equation and the corresponding initial and boundary conditions are represented by a series of deterministic partial differential equations which can be solved subsequently by a suitable numerical method. Some examples are given to show the reliability and efficiency of the proposed method.     

基于降雨空间变异的潜水运动随机模拟方法Ⅱ——条件模拟

建立了降雨空间变异条件下基于KLPC解法的潜水运动条件模拟方法，假设平面上若干测点的降雨量已知，分析了当随机模型中加入雨量站观测值时水头、流速和水动力弥散系数标准差的变化情况。研究结果表明：在条件模拟中，由于降雨协方差具有非平稳结构，需要采用数值解法来求解Fredholm方程；条件模拟方法计算出的水头、流速和水动力弥散系数的标准差要小于非条件模拟的结果；在降雨空间变异条件下，降雨的相关长度越大，方差越大，条件模拟对水头标准差削减越明显；与水头相比，条件模拟下流速和水动力弥散系数的标准差的消减更为明显，因此在考虑降雨的空间变异性时，条件模拟可减小溶质运移输入参数的不确定性具有一定作用。     

不均匀床沙组成及起动

文中首先应用概率统计方法研究不均匀床沙位置之间相互遮蔽的关系，并将暴露度的概念引入不均匀床沙的研究中，然后再根据暴露度并结合底速的随机脉动探讨了床沙起动的规律。计算结果表明，这种方法较符合实际。     

堤防渗流场参数敏感性三维随机有限元分析

采用随机有限元分析方法,研究了长江荆南干堤的三维各向异性非均质稳定随机渗流场中的随机参数和随机边界条件对渗流场模拟结果的影响,并进行敏感性分析.通过统计模拟和假设检验,建立并验证了该干堤渗流场内服从独立正态分布的渗透系数张量;讨论了堤防土层的地质结构特性、堤防渗透变形及破坏的特征、堤防渗透参数的敏感性;研究了上、下游水头随机边界条件、垂直防渗边界条件以及减压(导渗)沟随机特性的敏感性.实现了对渗流场的全面随机模拟和分析,得到的结论通过统计检验,并根据实测工程数据对照证明是可靠的.     

STOCHASTIC ANALYSIS OF UNSATURATED FLOW WITH THE NORMAL DISTRIBUTION OF SOIL HYDRAULIC CONDUCTIVITY

Stochastic approaches are useful to quantitatively describe transport behavior over large temporal and spatial scales while accounting for the influence of small-scale variabilities. Numerous solutions have been developed for unsatu-rated soil water flow based on the lognormal distribution of soil hydraulic conductivity. To our knowledge, no available stochastic solutions for unsaturated flow have been derived on the basis of the normal distribution of hydraulic conductivity. In this paper, stochastic solutions were developed for unsaturated flow by assuming the normal distribution of saturated hydraulic conductivity ( K,). Under the assumption that soil hydraulic properties are second-order stationary, analytical expressions for capillary tension head variance (σh2) and effective hydraulic conductivity (Kii*) in stratified soils were derived using the perturbation method. The dependence of σh2 and K," on soil variability and mean flow variables (the mean capillary tension head and its temporal and sp     

Three-dimensional stochastic seepage field for embankment engineering

Owing to the complexity of get-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smimov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.     

随机质点瞬时加速度谱的构建方法探讨

基于随机过程理论、应用统计学、随机信号分析理论,通过试验实时量测了5种不同流量条件下,顶冲角度分别为83.87°、54.82°、21.71°、2.24°时,不同断面水深对应的60余组瞬时流速信号,构建了随机质点瞬时流速概率模型,并以此推出了随机质点瞬时加速度谱概率模型及随机波列模拟方法。结果表明:基于赖斯白噪声理论的波动模拟新方法构建随机质点瞬时流速概率模型精准可靠,推求的随机质点瞬时加速度谱真实有效。     

广义Bayes法在裂隙岩体渗透系数随机反演中的应用

工程中由于存在各种随机因素,采用确定性的渗流分析方法进行渗透系数的反演必然会导致结果的不确定性.本文基于渗流场的随机有限元分析方法,结合变尺度优化算法和广义Bayes法,建立了一种渗透系数的随机反演方法,推导了详细的计算公式.该方法不仅考虑量测水头、渗透系数的随机性,还考虑了边界水头的随机性,不仅可以获得渗透系数的均值反演结果,还可以得到标准差的反演结果.最后将该法应用于重力坝坝基渗流算例分析中,以渗流有限元正分析计算结果作为"假想"的实测点水头值,通过随机反演,同时获得渗透系数均值与标准差的反演结果,将输入信息与反演结果对比分析,验证了渗透系数和标准差反演结果的正确性.     

基于随机微分方程的流域汇流模型

摘要：针对水文过程中存在的许多随机不确定性因素,本文以Nash模型为基础,利用随机微分方程理论,在确 定性汇流模型中引入随机输入项,建立了输入具有白噪声特性的随机Nash汇流模型,求解得到出流过程均值和 方差的解析解和数值解,并利用出流过程的均值和方差确定各时刻出流过程的概率分布。该方法借助于各时刻的 方差得到流量过程的分布概率,从而考虑预报的不确定性,为防洪决策提供预报值的不确定度,有利于降低水库 调洪风险率。     

平交口门区水动力特征试验研究

平原河网地区河道纵横交错,平交口门区("+"型交汇区)水流受交汇河道共同影响,水动力特征复杂。以新沟河三山港—武进港与京杭运河平交口门区为例,对其水动力特征进行了试验研究,并探讨了不同边界条件下的变化规律。受三山港吸流影响,京杭运河来流流至三山港口门时水流明显左偏并进入三山港,出现一定范围的横流区;受武进港出流顶托作用,位于武进港出口上游的运河右侧出现一较大范围的回流区,其范围随着武进港出流流速的减小而减小。河道边界对口门区水动力特征存在明显影响,流速较大一侧边界条件的改变对水动力特征的影响最明显。在类似平交口门区,需改变流速分布时,可优先考虑调整流速较大侧边界。     

FIRST ORDER WALL VORTICITY FORMULA UNDER IRREGULAR MESH

In the engineering applications, flow problems with complicated geometrical shape of boundaries are of ten happen. Their boundary conditions should be given in precisely when doing the simulation of these type of flows because the regions near to the boundaries generally play an important role on the defined solutions. Using the vorticity-stream function form of the N-S equations as governing equations in the flow field simulation with irregular mesh, the determining/calculating wall vorticity under irregular mesh is very important. In this paper, one first order formula of wall vorticity under irregular mesh was derived based on the 2-D Taylor expansion and was tested numerically through an example of a flow with the Z type, shape of boundaries. A satisfactory result was found which was compared with one obtained by FEM.     

筒装料管道车在不同流量下运动时水力特性研究

为探寻筒装料管道车水力输送的较优输送流量,采用模型试验与理论分析相结合的方法,分析了管道车在不同流量条件下运动时的水力特性。试验结果表明:同一型号的管道车在运动过程中,对某一特定的管道断面而言,流量越大,管道断面中的测压管水头越高;对于同一断面,流量越大,管道车车速也就越大,越早通过这个断面,断面测压管水头也就越早发生变化;流量大小变化不影响管路沿程测压管水头的下降趋势,无论管道车运动到哪个断面,这种整体下降趋势都不会改变,只是下降的幅度不同;而输送效率随流量的增加表现出先增大后减小的趋势。研究成果可为寻求较优的输送流量提供参考。     

随机波浪边界层的数值模拟与分析

该文基于雷诺平均的Navier-Stokes方程和k-ω两方程紊流模型建立了随机波浪边界层数学模型,模拟了粗糙底床上方的随机波浪边界层流速、床面剪切应力和紊动能量分布,计算结果与实测数据吻合良好。探讨了随机波浪边界层水动力特性,发现随机波浪时间序列中各个子波的紊动能量近似随该子波均方根自由振荡速度平方的增大而线性增大,但各个子波的紊动能量还受到上一个子波紊动能量传递的影响,体现了随机波浪与规则波浪的区别。整个随机波浪时间序列的有效摩阻系数和单个子波的摩阻系数均与前人实验数据和经验公式较为一致。     

渗透系数空间相关性对渗流场统计特征影响分析

渗透系数的空间变异性是影响渗流场不确定性的重要因素。将渗透系数作为各向同性对数正态平稳随机场,通过数值模拟研究渗透系数空间相关性对渗流场统计特征的影响。选取了3种具有代表性的相关函数模型,即指数模型、高斯模型和球状模型,分别以渗透系数的相关距离和变异系数为变化因子对水头方差作敏感性分析。结果表明,渗透系数相关函数模型的选取、相关距离和变异系数的取值对水头方差具有较大影响。     

AN EXTENDED MODELING OF TIDE-WAVE MOTION

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运行工况对水轮机活动导叶表面泥沙浓度分布的影响

采用标准k-ε模型对水轮机内部沙水流动进行数值模拟,研究了不同工况下映秀湾电站活动导叶泥沙分布情况.研究结果表明,活动导叶磨损主要集中在头部且工作面比背面磨损量大,泥沙颗粒在活动导叶底部有堆积.活动导叶泥沙绕流速度分布规律相似,并随着出力的增加头部绕流速度明显增大.     

侧向有界条件下垂向环流井水动力场模拟

分析现有的侧向无界条件下垂向环流井水动力场数学模型与解析解,基于MODFLOW建立侧向有界条件下的数值模型,模拟多组不同抽注流量和抽注段间距的情景,绘制水头误差分布图、前向追踪流线图和地下水流量占比图,通过对比分析论证了侧向边界对水头、流线形态和流量占比的影响。结果表明:随着流量增大以及抽注段间距增大,垂向环流井水动力场循环范围增大,边界对垂向环流井水动力场影响逐渐明显,流线越接近侧向边界,其形态由椭圆形趋近于矩形,且最外围均衡区内地下水交换量占比降低趋势明显;提出无量纲参数,进一步定量地分析侧向边界对流场的影响。     

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.