在蒸发条件下土壤水盐运动的数值模拟

本研究对土壤中水盐运动对流扩散方程进行了数值计算。利用省时的一阶精度的特征-分步法及使对流项作保留迎风特性的二阶精度的差分法,对在蒸发条件下土壤盐分向上运动积盐过程进行模拟,两个方法的计算结果与实验结果总体上都重合较好。     

对流边界层大涡自组织过程的数值研究

利用简化的边界层日变化干对流模式,结合非线性热力学观点,数值模拟并分析了日间对流边界层中大涡形成、发展及衰亡的动力和热力学特征.结果表明,对流边界层中大涡始终处于不稳定状态,大涡的自组织合并和破碎串级输送过程同时并存,前者与边界层系统的局部减熵相对应,后者与对流边界层的总体增熵效应对应;大涡的演变是对流边界层总体增熵这一稳定因素和局部减熵这一不稳定因素相互竞争的结果.     

大变形轴向运动梁的精确动力学模型

轴向运动梁的横向振动是具有实际工程背景的动力学问题.该文应用Cosserat弹性杆模型讨论圆截面轴向运动梁的动力学建模及其运动稳定性.以沿梁中心线的弧坐标代替方向固定的坐标轴,根据梁截面的姿态随弧坐标和时间的变化确定梁的变形过程.从欧拉的速度场概念出发,考虑梁截面转动的惯性效应和剪切变形,建立大变形轴向运动梁的动力学方程.其小变形特例为轴向运动的三维Timoshenko梁.基于该模型分析了轴向运动梁准稳态运动的静态和动态稳定性,导出可导致失稳的临界轴向速度.证明空间域内的欧拉稳定性条件是时间域内的Lyapunov稳定性的必要条件.      

基于参考信号的广义特征值分解盲源分离算法及其在北斗多路径效应削弱中的应用

多路径误差是北斗导航定位系统高精度动态监测的主要误差源。针对北斗导航定位系统多路径误差的特性,结合广义特征值盲源分离方法的优势,提出一种基于参考信号的广义特征值盲源分离算法来削弱多路径效应的影响。首先将前一天的原始坐标残差序列通过奇异谱分析方法进行去噪,其结果作为初始参考信号;然后将当天的原始坐标残差序列进行经验模式分解方法分解,分解得到的IMF分量作为虚拟观测数据,利用广义特征值盲源分离算法获取当天多路径误差信号;最后,利用仿真数据和连续10天的实际观测数据进行试验分析,结果表明利用该方法建立的多路径误差改正模型能有效地了削弱多路径的影响,北、东、天三个方向精度分别提高了78.8%、35.3%、90.1%。提出的模型在一定程度上解决了固定多路径模型随着时间推移重复性减小且有效性降低的问题。     

光纤陀螺光纤敏感线圈三维温度瞬态响应模型

针对光纤敏感线圈的热致非互易相移问题,通过传热分析建立了光纤敏感线圈的三维温度瞬态响应模型.利用该温度瞬态响应模型全面分析了三维坐标下的温度梯度造成的热致非互易效应;结合光纤陀螺实际的工作环境,利用仿真对四极对称绕法的光纤环进行了分析,获取了温度激励造成的热致速率误差.通过温度模型计算的热致误差速率与温箱中光纤陀螺稳测数据的极差为0.48(°)/h,计算结果验证了光纤敏感线圈三维温度瞬态响应模型的有效性.利用该模型可有效指导光纤环热结构参数的设计,从而抑制光纤环的Shupe误差,提高光纤陀螺的温度性能.     

磁场对双扩散液层热毛细对流的影响

通过数值模拟的方法对磁场作用下的双扩散液层热毛细对流进行了研究, 模型中同时考虑了热毛细效应和溶质毛细效应的存在. 研究结果显示, 外部磁场能够有效削弱液层内热毛细对流的强度, 改变热毛细对流的对流结构; 随着磁场强度的增大, 液层内热毛细对流的对流强度逐渐减小, 热质传递过程中扩散效应逐渐得到增强; 最终, 溶质浓度沿水平方向呈梯度分布. 因此, 当磁场强度足够大时能够实现晶体生长中所需的纯扩散条件.     

灌溉诱发高速黄土滑坡的运动机理

针对黄土高原灌溉诱发的高速黄土滑坡所出现的各种迹象, 本文建立了滑坡体的运动模型。利用变分原理推导出了滑坡体的滑动轨迹、滑速、滑距以及黄土泥流 (液化物质)的流速公式。用这些公式对刘家峡、盐锅峡及八盘峡库区黑方台高速黄土滑坡群发生的全过程进行了模拟计算, 其结果与实际情况-致。     

基于消能井井深变化下水力特性的研究

研究了消能井内消能工井深变化对各水力参数的影响。试验在中部进流时,消能井直径D、通气孔直径d、出口高度h、短压力段坡比l固定的情况下,通过改变消能井井深来研究井深对流态、压强、不均匀程度的影响,最后通过对脉动压强和系统消能率的比较分析来研究井深变化时各水力特性规律及消能井井深的合理取值。本次试验采用4种井深的变化,综合多次水头变化来研究井深变化对水力特性的影响。试验结果表明:对于同一堰上水头,相对水垫深度h_j/D_0随井深波动变化,在井深H_0/D_0=1.5时水垫深度达到最大,压强及其波动的不均匀程度也最小,所以本模型拟采用井深H_0/D_0=1.5最为合理。     

入水问题的Euler-Lagrange流固耦合数值模以技术研究

针对结构入水过程的特点,建立了一种把Eulerian计算过程和Lagrangian计算过程耦合起来的数值技术,编写了计算程序,把结构对水作用的过程和结构动力学响应过程的计算结合起来,实现了结构与水之间流固耦合作用过程的模拟.其中水、空气的运动利用Eulerian过程的流体弹塑性有限差分计算程序进行模拟,结构的运动变形利用Lagrangian过程的结构动力学有限元计算程序模拟结构响应.通过板入水问题的计算结果与商业软件计算结果进行比较,验证了计算方法对流固间相互作用处理的正确性.本文计算程序可用于一般入水问题的结构响应-流场运动分析中.     

用物理黏性构建高阶不振荡对流扩散差分格式

利用数值摄动算法, 通过扩散格式数值摄动重构把对流扩散方程的2阶中心差分格式(2-CDS)重构为高精度高分辨率格式, 解析分析和模型方程计算证实了新格式的高精度不振荡性质. 新格式是把物理黏性使流动光滑化的扩散运动规律引入2-CDS 中的结果. 该法显然与构建高级离散格式的常见方法不同. 证实: 数值摄动重构中引入扩散运动规律的结果格式与引入对流运动规律(下游不影响上游的规律)的结果格式一致, 说明对离散方程的数值摄动运算, 在维持原格式结构形式不动的条件下, 不仅能提高格式精度和稳健性, 且可揭示对流离散运动规律与扩散离散运动规律之间的内在关联;同时证实, 文中提出和使用的上、下游分裂方法是构建高精度不振荡离散格式的一个有效方法.     

Water and salt movements in simultaneous flood-irrigation and well-drainage operations

This paper describes a new technology for solonchak soil reclamation in which surface flood irrigation of fresh water and pumped wells drainage of salty groundwater are combined. The comprehensive investigation of water and salt movement has been conducted through field test, laboratory simulation and numerical calculation. The dependence of desalination on irrigation water quantity, drainage quantity, leaching time and other parameters is obtained based on the field tests. The entire desalination process under the flood-irrigation and well-drainage operations was experimentally simulated in a vertical soil column. The water and salt movement has been numerically analyzed for both the field and laboratory conditions. The present work indicates that this new technology can greatly improve the effects of desalination. The project supported by the National Natural Science Foundation of China     

The numerical analysis of water and solute movement in scale heterogeneous profiles

A computer based numerical method is presented for the analysis of water and solute movement in unsaturated heterogeneous porous materials. Such a method is necessary since, for those field studies where solute movement is of concern, the soil profiles under consideration are invariably heterogeneous. The numerical analysis is based on a general one-dimensional finite difference soil water flow model which includes a numerical technique combining the concepts of scale heterogeneity with an interpolative soil water hysteresis model. An explicit finite difference solute movement subroutine is incorporated into the unsaturated flow model to describe the transport of nonreactive solutes. A velocity dependent longitudinal dispersion coefficient is used in the solution of the hydrodynamic dispersion equation. The resulting hysteretic scale heterogeneous solute movement model permits the study of solute dynamics during infiltrating and redistribution in realistically complex spatially varying soil profiles. Results are presented for the leaching of both coarse grading to fine and fine grading to coarse sand profiles. Both vertical and horizontal profiles are studied using either a constant flux or a constant concentration input boundary condition. The four cases studied demonstrate the versatility of the numerical method and emphasise the substantial differences in transport behavior that can arise between heterogeneous and homogeneous profiles.Now with BHP Petroleum Pty. Ltd., GPO Box 1911R, Melbourne, Vic. 3001, Australia.     

正交各向异性地基平面问题动力响应研究

以位移分量为基本未知量,在直角坐标系下建立正交各向异性地基的平面应变问题动力偏微分方程．采用Laplace-Fourier变换和逆变换方法,引入初始条件和边界条件,推导了任意形式表面动荷载作用下正交各向异性地基平面问题在时域内动力反应的积分形式解．基于理论解,编制了相应的计算程序,并对正交各向异性土
体表面作用线性移动谐振荷载进行了算例分析,研究了土体参数、荷载移动速度、荷载频率不同而导致的土体表面各点竖向位移幅值的变化规律,以及荷载速度对竖向应力分量的影响规律．数值分析结果表明：土体的各向异性、荷载频率和移动速度对表面位移幅值有较大影响,土体阻尼比对于荷载中心点附近的位移幅值影响较小;荷载移动速度对于竖向应力分量有较大影响,这对工程实践具有重要指导意义．     

Effect of quadratic pressure gradient term on a one-dimensional moving boundary problem based on modified Darcy’s law

A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy’s flow problem, the exact analytical solution for the case of Darcy’s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.     

Migration of salts with the leaching of soils with piecewise-homogeneous salinization

The article discusses the one-dimensional problem of the leaching of a soil with piecewise-homogeneous initial salinization under conditions of a movable wetting front. Depending on the character of the salinization and the water-physical properties of the soil at the moving boundary, there are given either the values of the sought function or of its derivative with respect to the spatial variable. The solution of the problem is represented as the superposition of solutions of an auxiliary process modelling the process of the leaching of a soil with homogeneous salinization with the presence of an upper desalinated layer. A numerical example is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 76–81, May–June, 1977.     

Turbulent air flow over a moving curved surface

A numerical model of turbulent air flow over a curved surface is described. The model is based on two-dimensional nonlinear Reynolds equations and continuity equations written in a coordinate system moving with the profile of the curved surface. The Reynolds stresses are represented in the form of the product of the isotropic turbulent viscosity coefficient, which increases linearly with height, and the deformation tensor of the mean velocity field. Flow over a stationary sinusoidal surface and a sinusoidal gravity wave on water is simulated. The structure of the velocity and pressure wave fields is obtained. The differences in flow over stationary and moving surfaces are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–24, September–October, 1986.     

Modeling of cementitious materials exposed to isothermal calcium leaching,considering process kinetics and advective water flow. Part 2: Numerical solution

The second part of the paper presents numerical solutions of the mathematical model of hydro-chemo-mechanical behavior of cementitious materials exposed to contact with deionized water of part 1. The model defines kinetics of the calcium leaching process instead of a direct application of a curve describing equilibrium between solid calcium in the material skeleton and the calcium dissolved in the pore solution. It further takes into account the advective flux of calcium ions. Both aspects are new as compared to previous models. The weak form of the governing equations of the model is derived first using the Galerkin method. Then, the equations are discretized in space with finite elements and in time domain with finite differences, and finally the procedures used for numerical solution of their discretized form are presented. Three numerical examples are solved to test the numerical solution procedure proposed and demonstrate its robustness for solution of 1D and 2D problems concerning fast and slow leaching of cement-based materials. The effect of various factors on the results concerning chemical degradation of structures made of cementitious materials is analyzed as well.     

低渗透多孔介质渗流动边界模型的解析与数值解

考虑启动压力梯度的低渗透多孔介质非达西渗流模型属于强非线性动边界问题, 分别利用相似变量变换方法和基于空间坐标变换的有限差分方法, 对内边界变压力情况下、考虑启动压力梯度的一维低渗透多孔介质非达西渗流动边界模型进行了精确解析与数值求解研究. 研究结果表明:该动边界模型存在唯一的精确解析解, 且所求得的精确解析解可严格验证数值解的正确性;且当启动压力梯度值趋于零时, 非达西渗流动边界模型的精确解析解将退化为达西渗流情况下的精确解析解. 由求解结果作出的非零无因次启动压力梯度下的地层压力分布曲线表现出紧支性特点, 其与达西渗流模型的有显著不同. 因此, 研究低渗透多孔介质中非稳态渗流问题时, 应该考虑动边界的影响. 研究内容完善了低渗透多孔介质的非达西渗流力学理论, 为低渗透油气藏开发的试井解释与油藏数值模拟技术提供了理论基础.      

Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves

Potential function and complex function in the elliptic coordinate system are employed to solve the problem of scattering harmonic plane waves by multiple elliptic cavities in water saturated soil medium. The steady state Biot’s dynamic equations of poroelasticity are uncoupled into Helmholtz equations via given potentials. The stresses and pore water pressures are obtained by using complex functions in elliptic coordinates with certain boundary conditions. Finally, the dynamic stresses for the case of two interacting elliptic cavities are obtained and discussed in details via a numerical example.