用局部间断伽辽金有限元法分析渗流场

把局部间断伽辽金有限元法(LDG)运用到渗流分析中,编制了LDG法渗流分析的计算程序,运用该程序对均质或非均质渗流场分布进行分析,把所得结果与解析解或一般有限元法所得结果进行比较,证明LDG法在渗流分析中是十分有效的。     

A spacetime discontinuous Galerkin method for the two-dimensional unsteady convection-dispersion problems

The unsteady two-dimensional convection-diffusion (CD) equation, which is the governing equation of the unsteady two-dimensional convection-dispersion problem, as the water contamination problems, has a mixed hyperbolic-parabolic character. When the equation has a strong mixed hyperbolic character, the exact solution is nonsmooth. In this case, the conventional numerical methods give approximate solutions which either oscillate or smear out the sharp front of the exact solution. The spacetime discontinuous Galerkin method (STDGM) is an extention of the space discontinuous Galerkin method (SDGM), applying the discontinuity in the time direction, as well as in space. Both these methods are respective modifications of the standard Galerkin finite element method (SGM). In this paper, the STDGM is applied to solve the CD equation, when the Péclet number has extremely high values, which means a strong mixed hyperbolic character. With this method, three artificial diffusion terms are introduced by modifying the test functions of the finite element method. These functions include the discontinuity int, x andy axis. The results obtained from the analytical solution of the problem are used for testing the numerical solution, applying both the space-discontinuous Galerkin method (SDGM) and the STDGM and are presented in diagrams, from which useful observations, comparisons and conclusions can be drawn.     

MODELING DAM-BREAK FLOOD OVER NATURAL RIVERS USING DISCONTINUOUS GALERKIN METHOD

A well-balanced numerical model is presented for two-dimensional, depth-averaged, shallow water flows based on the Discontinuous Galerkin (DG) method. The model is applied to simulate dam-break flood in natural rivers with wet/dry bed and complex topography. To eliminate numerical imbalance, the pressure force and bed slope terms are combined in the shallow water flow equations. For partially wet/dry elements, a treatment of the source term that preserves the well-balanced property is presented. A treatment for modeling flow over initially dry bed is presented. Numerical results show that the time step used is related to the dry bed criterion. The intercell numerical flux in the DG method is computed by the Harten-Lax-van Contact (HLLC) approximate Riemann solver. A two-dimensional slope limiting procedure is employed to prevent spurious oscillation. The robustness and accuracy of the model are demonstrated through several test cases, including dam-break flow in a channel with three bumps, laboratory dam-break tests over a triangular bump and an L-shape bend, dam-break flood in the Paute River, and the Malpasset dam-break case. Numerical results show that the model is robust and accurate to simulate dam-break flood over natural rivers with complex geometry and wet/dry beds.     

A fully-explicit discontinuous Galerkin hydrodynamic model for variably-satu- rated porous media

Groundwater flows play a key role in the recharge of aquifers, the transport of solutes through subsurface systems or the control of surface runoff. Predicting these processes requires the use of groundwater models with their applicability directly linked to their accuracy and computational efficiency. In this paper, we present a new method to model water dynamics in variably- saturated porous media. Our model is based on a fully-explicit discontinuous-Galerkin formulation of the 3D Richards equation, which shows a perfect scaling on parallel architectures. We make use of an adapted jump penalty term for the discontinuous-Galerkin scheme and of a slope limiter algorithm to produce oscillation-free exactly conservative solutions. We show that such an approach is particularly well suited to infiltration fronts. The model results are in good agreement with the reference model Hydrus-lD and seem promising for large scale applications involving a coarse representation of saturated soil.     

Effect of channel shape on selection of time marching scheme in the discontinuous Galerkin method for 1-D open channel flow

One-dimensional open channel flows are simulated using the discontinuous Galerkin finite element method. Three different explicit time marching schemes, including multistep/multistage schemes, are evaluated for different channel shapes for accuracy and efficiency. The Forward Euler, second-order Adam-Bashforth(multistep), and second-order total variation diminishing(TVD) Runge-Kutta(multistage) time marching schemes are utilized. The role of monotonized central, minmod, and zero TVD slope limiters for each of the time marching scheme is investigated. The numerical flux is approximated using HLL function. The accuracy and robustness of different time marching schemes are evaluated for steady and unsteady flows using analytical and measured data. The unsteady flows include dam break tests with wet and dry beds downstream of the dam in prismatic(rectangular, trapezoidal, triangular, and parabolic cross-sections) and non-prismatic(natural river) channels. The steady flow test involves simulation of hydraulic jump in a diverging rectangular channel. The various schemes are evaluated by comparing accuracy using statistical measures and efficiency using maximum possible time step size as well as CPU runtime. The second-order Adam-Bashforth time marching scheme is found to have the best accuracy and efficiency among the time stepping schemes tested.     

基于无单元Galerkin法的饱和—非饱和土石坝渗流正演模拟

在土石坝渗流正演模拟中,仅研究饱和区域的渗流场并不能全面真实地反映出土石坝地下渗流状态,非饱和渗流区域的研究同样至关重要,利用无单元Galerkin法对饱和-非饱和渗流域进行求解。首先从达西定律出发,推导了渗流方程及边界条件,其中详细推导了无单元Galerkin法——通过滑动最小二乘法构造形函数,同时利用罚函数的方法计算边界条件。然后,通过与GeoStudio软件计算出的仅饱和渗流场以及饱和-非饱和渗流场进行比较,证明了该方法的准确性及有效性。最后,通过不同的均质和非均质模型,研究了坝体中零压力线、水头值、孔隙压力、含水率的分布。无单元Galerkin法只需要通过节点来实现对全域渗流场的精确逼近,解决了对网格单元的依赖问题,与其他数值方法相比,其具有前期处理数据简单和精度高的优点,更适合稳定饱和-非饱和渗流场这种复杂情况的正演模拟。     

应用三维无单元伽辽金法追踪裂纹扩展

本文应用三维无单元伽辽金法追踪裂纹扩展。将可视准则推广到三维以处理三维不连续面对积分点影响域的影响,同时考虑不连续面刚度对整体平衡方程的贡献。利用单点位移公式计算裂纹前缘应力强度因子,假设裂纹在法平面内扩展,采用最大能量释放率判据作为三维复合型裂纹扩展判据,编制EFGM3D程序实现对线弹性体中三维准静态裂纹扩展的追踪。通过对含半币形表面裂纹的立方体算例的分析,证明本文方法和程序在裂纹扩展模拟上是合理有效的。     

三维无单元伽辽金法及其在拱坝分析中的应用

本文介绍了三维无单元伽辽金法的基本理论,并将其应用于拱坝结构分析中,基于变分原理推导出三维线弹性无单元伽辽金法的整体平衡方程。为了处理实际水利工程中断层、宏观裂纹等不连续情况,采用可视准则处理不连续面对积分点影响域的影响,同时考虑不连续面两表面相互作用对整体平衡方程的贡献。编制了三维无单元法计算程序并用以分析拉西瓦水电工程拱坝一地基系统模型,结果表明,其反映了拱坝在水荷载作用下的位移分布规律。     

流体力学广义 GLS/PG 方法基本理论

本文在分析总结国内外有关研究的基础上，讨论了以Petrov-Galerkin原理为基础求解Navier-Stokes方程的广义GLS／PG（Galerkin-Least-Square/Petrov-Galerkin)方法基本理论。文中首先以对流－扩散方程为例说明了Petrov-Galerkin方法的基本原理，然后给出了流体力学广义GLS／PG方法基本理论，而且说明了SUPG法和PSPG法等均是其中的一种方法，从而可以从更系统，广泛的角度来分析研究相应理论的基本性质和特点。     

Simulation of flow in compound open-channel using a discontinuous Galerkin finite-element method with Smagorinsky turbulence closure

The small-scale spatial variability of eddy viscosity which is characteristic for the turbulent shear stress in compound open-channel flows was studied and investigated in this paper. Different options including a constant value, zero-equation, one-equation, two-equation, and Smagorinsky turbulence models for parameterizing the eddy viscosity were developed in the framework of the discontinuous Galerkin finite-element SLIM model and applied for presenting the complex velocity profile in two different experimental data sets of laboratory flumes. A very good qualitative agreement was achieved between numerical results and measurement data for both velocity and flow depth of all experimental data sets in general. In addition, the calculation results showed that the turbulent Smagorinsky empiricism allowed a better presentation of non-uniform velocity in the floodplain and transition regions between plain and main channels than the others in all calculated cases. This empiricism predicted a very close variation of eddy viscosity in comparison with the results calculated by the depth-averaged Reynolds' stress and the lateral gradient of longitudinal velocity. The eddy viscosity varies significantly in the channel section; in particular the small values often occurred around the middle location of floodplains and the central location of the main channel while the large values appeared in the transition regions, presenting different minimum and maximum values of eddy viscosity in each flow region. The effects of eddy viscosity variation on lateral distribution of velocity profile were also investigated and discussed.     

Comparative study of MPS method and level-set method for sloshing flows

This paper presents a comparative study of a meshless level-set method in the simulation of sloshing flows. The numerical moving particle semi-implicit （MPS） method and a grid based schemes of the MPS and level-set methods are outlined and two violent sloshing cases are considered. The computed results are compared with the corresponding experimental data for validation. The impact pressure and the deformations of free surface induced by sloshing are comparatively analyzed, and are in good agreement with experimental ones. Results show that both the MPS and level-set methods are good tools for simulation of violent sloshing flows. However, the second pressure peaks as well as breaking and splashing of free surface by the MPS method are captured better than by the level-set method.     

Numerical study of the wave-induced slamming force on the elastic plate based on MPS-FEM coupled method

Slamming is the phenomenon of structure impacting the water surface. It always results in the extremely high load on the structure. This paper is mainly concerned with the slamming force caused by the wave-plate interaction. In this paper, the process of solitary wave impacting onto the horizontal plate is simulated with the help of the moving particle semi-implicit and finite element coupled method(MPS-FEM). The MPS method is adopted to calculate the fluid domain while the structural domain is solved by FEM method. In the first series of simulations, the profiles of the solitary waves with various amplitudes, which are generated in the numerical wave tank, are compared with the theoretical results. Thereafter the interaction between the solitary waves and a rigid plate is simulated. The effects of wave amplitude, as well as the elevation of the plate above the initial water level, on the slamming force are numerically investigated. The calculated results are compared with the available experimental data. Finally, the interactions between the solitary waves and the elastic plate are also simulated. The effects of the structural flexibility on the wave-induced force are analyzed by the comparison between the cases with elastic and the rigid plate.     

Numerical modeling of dam-break flood through intricate city layouts including underground spaces using GPU-based SPH method

This paper applies the meshfree Smoothed Particle Hydrodynamics （SPH） method with Graphical Processing Unit （GPU） parallel computing technique to investigate the highly complex 3-D dam-break flow in urban areas including underground spaces. Taking the advantage of GPUs parallel computing techniques, simulations involving more than 107 particles can be achieved. We use a virtual geometric plane boundary to handle the outermost solid wall in order to save considerable video card memory for the GPU computing. To evaluate the accuracy of the new GPU-based SPH model, qualitative and quantitative comparison to a real flooding experiment is performed and the results of a numerical model based on Shallow Water Equations （SWEs） is given with good accuracy. With the new GPU-based SPH model, the effects of the building layouts and underground spaces on the propagation of dambreak flood through an intricate city layout are examined.     

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.     

横观各向同性岩体地基中赋存裂纹断裂力学分析

采用无双材料对偶边界元方法分析了半无限横观各向同性岩体地基中赋存的正方形裂纹,裂 纹面上作用着法向均布力,横观各向同性岩体地基的各向同性面平行于半无限域自由面。数值计算得 到了该类裂纹的应力强度因子值。根据数值结果讨论了横观各向同性岩体地基弹性参数、裂纹面对各 向同性面的倾角赋存裂纹应力强度因子的影响。结果表明,岩体地基弹性系数、裂纹面对各向同性面的 倾角对裂尖应力强度因子有明显影响。在弹性系数中,弹性模量对应力强度因子的影响最为敏感。     

快速涡方法中自适应树算法与涡量插值方法的研究

快速涡方法计算过程中占用过多内存资源,网格重置时用的插值方法具有一定的缺陷。该文通过预先判断自适应树节点数量等方式,生成新的自适应树构造方法;通过利用面积权重和距离相结合的方式重新构造了涡量插值方法。计算结果表明,改进的涡方法得到的计算结果更加精确,同时大大节省了计算所需的内存空间。     

A numerical study on dispersion of particles from the surface of a circular cylinder placed in a gas flow using discrete vortex method

The dispersion of particles emitted from the surface of a circular cylinder placed in a gas flow at the Reynolds number of 200 000 is numerically investigated using the discrete vortex method coupled with a Lagrangian approach for solid particle tracking. The wake vortex patterns, the temporal-spatial distributions and trajectories as well as the dispersion functions for particles with various Stokes numbers（St） ranging from 0.001 to 1.0 are obtained. The numerical results reveal that：（1） Solid particles on the cylinder surface are picked up and then transported away from the cylinder by the wake vortex flow.（2） Solid particles emitted from the cylinder surface always follow the vortices in the cylinder wake, and the response of particles to wake vortices is directly related to their Stokes numbers（particles with St= 0.001, 0.0038, 0.01 can distribute both in the vortex core and around the vortex periphery, whereas those with St= 0.1, 1.0 can not enter the vortex core and congregate mainly around the vortex periphery）.（3） The particles move in rolling state in the wake region, and the dispersion intensity of particles in the lateral direction decreases remarkably as the Stokes number of particles is increased from 0.001 to 1.0.     

The optimal retrieval of ocean color constituent concentrations based on the variational method

In this paper, a new approach to the optimal retrieval of the ocean color based on the variational method is developed by setting up a rational target functional combining with the Broydor Fletcher, Goldfarb, Shanno (BFGS) optimal algorithm. The numerical tests and the exemplary retrievals are carried out and compared with the statistical retrievals and the optimal retrievals based on the genetic algorithm. The results show that this approach enjoys a higher accuracy as compared to the statistical method and a higher efficiency as compared to the genetic algorithm. The optimal retrieval method presented in this paper provides a new idea for the ocean color inversion and could also be used as a reference for the direct assimilation of the satellite data into the ecological models.     

水电项目评标决策中的层次分析法

针对水电项目评标中常用方法存在的问题,将评标看成一个系统,把层次分析这一系统分析方法引用到水电项目评标决策中。层次分析法结构模型中结合专家的经验提出了评标决策的5项准则,通过判断矩阵为每一准则确定了相应权重,量化评标信息,最终为评标决策提供参考依据。     

Membrane finite element method for simulating fluid flow in porous medium

A new membrane finite element method for modeling fluid flow in a porous medium is presented in order to quickly and accurately simulate the geo-membrane fabric used in civil engineering. It is based on discontinuous finite element theory, and can be easily coupled with the normal Galerkin finite element method. Based on the saturated seepage equation, the element coefficient matrix of the membrane element method is derived, and a geometric transform relation for the membrane element between a global coordinate system and a local coordinate system is obtained. A method for the determination of the fluid flux conductivity of the membrane element is presented. This method provides a basis for determining discontinuous parameters in discontinuous finite element theory. An anti-seepage problem regarding the foundation of a building is analyzed by coupling the membrane finite element method with the normal Galerkin finite element method. The analysis results demonstrate the utility and superiority of the membrane finite element method in fluid flow analysis of a porous medium.