A moving mesh algorithm for 3-D regional groundwater flow with water table and seepage face

A numerical algorithm is described for solving the free-surface groundwater flow equations in 3-D large-scale unconfined aquifers with strongly heterogeneous conductivity and surface recharge. The algorithm uses a moving mesh to track the water-table as it evolves according to kinematic and seepage face boundary conditions. Both steady-state and transient algorithms are implemented in the SECO-Flow 3-D code and demonstrated on stratigraphy based on the Delaware Basin of south-eastern New Mexico.     

油水两相渗流多孔介质弹性波传播动力学模型研究

弹性波在储层渗流场中的传播与衰减规律是研究波场强化采油动力学机理的重要基础.基于等效流体理论和饱和静态流体弹性波传播Biot理论,建立油水两非混相流体渗流条件下储层多孔介质中弹性波传播的动力学模型,通过算例求解与分析,发现含油水两相渗流储层多孔介质中同时存在着3种纵波P1、P2、P3和1种横波S;受频率和含水饱和度的影响,各波波速和品质因子呈现出不同变化规律,4种体波波速与频率、饱和度正相关,P1、P2波品质因子与饱和度正相关,P3和S波品质因子与饱和度负相关;最后,通过与传统静态弹性波模型结果对比,进一步分析了宏观渗流场对弹性波传播特征的影响规律,为揭示低频人工地震波辅助强化采油技术的动力学机理和工艺参数优化提供了重要理论依据.

     

A 3-D finite element conjugate gradient model of subsurface flow with automatic mesh generation

The 3-D flow modelling of groundwater systems of realistic size generally requires a big effort for the preparation of the input data as well as large computational costs. A numerical finite element model (MAITHREE) is developed for the efficient analysis of the steady and unsteady behaviour of natural confined 3-D basins. Starting from an initial triangular grid the code automatically generates a set of tetrahedral elements in each of the geologic units or subunits specified by the user in the vertical profile. The original element incidences list is then rearranged in order to provide conforming 3-D elements throughout the domain. The model is designed with a view to saving much of the labour involved in setting a 3-D grid and to providing flexibility as well as economical convenience through a high computational efficiency. The latter task is achieved by the aid of a solver based on the modified conjugate gradient (MCG) method which has proved to be an excellent technique for the solution of large linear finite element sets of sparse 3-D subsurface equations. Some examples derived from both hypothetical and real-world situations are discussed to illustrate the innovative features of MAITHREE and its computational performance.     

A simple model for the formation of vegetated dunes

A simple model for the dynamics of dunes associated with vegetation is proposed. Using the model, the formation processes of transverse dunes, parabolic dunes and elongated parabolic dunes are simulated according to two environmental factors: (i) the amount of sand at the source; (ii) the wind force. The results have qualitative correspondence to the real counterpart, and the simplicity of the algorithm and the consequent ease of handling this model provide us with wide applicability for the investigation of the complex interplay between vegetation and dunes. Copyright © 2001 John Wiley & Sons, Ltd.     

A constitutive model for water flow in unsaturated fractured rocks

A conceptual model for describing effective saturation in fractured hard rock is presented. The fracture network and the rock matrix are considered as an equivalent continuum medium where each fracture is conceptualized as a porous medium of granular structure and the rock matrix is assumed to be impermeable. The proposed model is based on the representation of a rough‐walled fracture by an equivalent porous medium, which is described using classical constitutive models. A simple closed‐form equation for the effective saturation is obtained when the van Genuchten model is used to describe saturation inside fractures and fractal laws are assumed for both aperture and number of fractures. The relative hydraulic conductivity for the fractured rock is predicted from a simple relation derived by Liu and Bodvarsson. The proposed constitutive model contains three independent parameters, which may be obtained by fitting the proposed effective saturation curve to experimental data. Two of the model parameters have physical meaning and can be identified with the reciprocal of the air entry pressure values in the fractures of minimum and maximum apertures. Effective saturation and relative hydraulic conductivity curves match fairly well the simulated constitutive relations obtained by Liu and Bodvarsson. Copyright © 2008 John Wiley & Sons, Ltd.     

A 3D unstructured non-hydrostatic ocean model for internal waves

A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max–min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max–min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model’s capability to resolve internal waves relating to complex non-hydrostatic phenomena.     

A 3-D finite volume model for sediment transport in coastal waters

Ocean Dynamics - A 3-D model has been developed to simulate sediment transport and bed change induced by currents and waves in coastal waters. The currents are calculated with the 3-D...     

A method for canopy water content estimation for highly vegetated surfaces-shortwave infrared perpendicular water stress index

In this paper, a new method for canopy water content (FMC) estimation for highly vegetated surfaces- shortwave infrared perpendicular water stress index (SPSI) is developed using NIR, SWIR wavelengths of Enhanced Thematic Mapper Plus (ETM ) on the basis of spectral features and distribution of surface targets with different water conditions in NIR-SWIR spectral space. The developed method is further explored with radiative transfer simulations using PROSPECT, Lillesaeter, SailH and 6S. It is evident from the results of validation derived from satellite synchronous field measurements that SPSI is highly correlated with FMC, coefficient of determination (R squared) and root mean square error are 0.79 and 26.41%. The paper concludes that SPSI has a potential in vegetation water content estimation in terms of FMC.     

A cellular automata model of surface water flow

Previous cellular automata models of surface water flow have been constructed to reflect steady, gradually‐varied flow conditions. While these models are extremely important in showing the near‐equilibrium forms that result from the interactions of water and boundary material, highly dynamic forms and processes require models that represent unsteady flow conditions. In order to simulate unsteady flow in a cellular model of surface water flow, the conservation of mass and the Manning's equations are coupled with an algorithm to delay the movement of water from one pixel to the next until the correct timing is reached. This approach yields highly realistic flood wave hydrographs when compared with flood observations in the Walnut Gulch Experiment Watershed. Coupling this unsteady flow model with simple laws of sediment erosion, transport, and deposition should allow event‐based simulations of watershed and river channel geomorphologic change. Copyright © 2007 John Wiley & Sons, Ltd.     

三维分层流动过双山脉地形激发的大气船舶重力波动力学理论和数值试验

利用我们建立的三维分层线性理论计算模式和中尺度数值模式ARPS, 分别研究了三维分层流动过双山脉地形产生的三维线性和非线性山脉重力波和大气船舶的结构特征及其形成机制.线性理论计算结果表明三维三层流动过双山脉地形时,两个山脉各自强迫出一个发散模态的山脉背风波,在第二个山脉背风面,三维三层流动过双山脉地形可以强迫出两个发散模态的拦截背风波,大大加强了对大气环流的拖曳作用.非线性数值模拟结果表明,流动过山所产生的非线性山脉重力波和大气船舶完全不同于三维分层线性理论计算模式所产生的山脉重力波和大气船舶的结构和特征,由于分层流体之间的非线性相互作用,三维三层流动过双山脉地形时,可在第二个山脉背风面激发4个发散模态的拦截背风波. 三维三层流动过双山脉地形所强迫的山脉重力波和大气船舶,具有同三维三层流动过孤立山脉所产生的山脉重力波和大气船舶完全不同的结构和特征,三维流动过双山脉地形对两个山脉之间的距离表现出极大的敏感性.对于相距较远的两个山脉,流动过双山脉所强迫的山脉重力波表现为4个发散模态的拦截背风波,波动的能量相对于相距较近的两个山脉能传播到更高的高度.     

A stochastic model for 3-dimensional flow patterns in infiltration experiments

Modelling the 3-dimensional water flux at field scale is important for the design and the analysis of dye tracer experiments. Furthermore, it enables the estimation of the risk to groundwater by pollutants, and the visualisation and classification of flux patterns. A stochastic model is presented that allows for the modelling of a wide range of flow patterns in soils as they appear in dye tracer experiments. The leading idea is that infiltrating water runs along paths, not necessarily preferential ones, and water spreads into the soil uniformly from the paths into the matrix. The model is essentially based on a Poisson point process and three independent random fields. The point process defines the starting points of the paths at the surface. The values of two random fields determine the course of the paths. The third random field governs the depth of the infiltration front. As an extension of the model, we present two simulated examples for stratified soils.     

A preliminary model for 3-D rheological structure of the lithosphere in North China

3-D rheological structure is mainly the spatial distribution of lithospheric strength or viscos-ity, its strength and viscosity are indispensable parameters in quantitative study of the lithosphere deformation. Plate tectonics theory initially divided the…     

A linearized approach to flow resistance uncertainty in a 2-D finite volume model of flood flow

A linearized approach to quantifying predictive uncertainty in a 2-D model of shallow water flow in response to uncertainty in friction parameterization is presented. The resulting uncertain finite volume (UFV) method is tested against Monte Carlo simulations for uncertain models over channel only, floodplain only and channel and floodplain meshes. The results show that the UFV model performs well in predicting mean and standard deviations of water depths, for problems with two independent Manning's n values, with standard deviations of up to 0.02 m^1/3 s⁻¹ with a mean value of 0.03 m^1/3 s⁻¹. For depth averaged velocities, mean values are well represented, but standard deviations are poorly predicted by UFV. UFV also performs well when modelling flow over an uneven fractal topography and for a distributed (11 degrees of freedom) parameterization. A computation time advantage of >50 when compared to the Monte Carlo method is observed.     

1-D, 2-D, and 3-D analytical solutions of unsaturated flow in groundwater

An excellent tool for checking numerical models of unsaturated flow in groundwater is analytical solutions. However, because of the highly nonlinear nature of the governing partial differential equation, only a limited number of analytical solutions are available. This paper first gives some simple 1-D solutions. Next, by use of a transformation, the nonlinear partial differential equation is converted to a linear one for a specific form of the moisture content vs. pressure head and relative hydraulic conductivity vs. pressure head curves. This allows both 2-D and 3-D solutions to be derived, which is done in this paper. Finally, computations from a finite element computer program are compared with results from one of the analytical solutions to illustrate the use of the derived equations.     

傅里叶有限差分法三维波动方程正演模拟

傅里叶有限差分(FFD)法兼有相位屏法和隐式有限差分法二者的优势,能够处理复杂地质构造中的波传播问题,但在三维情形下,算子的双向分裂会引起明显的方位各向异性误差.本文用Fourier变换计算双向分裂过程中的高阶交叉项,消除了方位各向异性误差.该方法充分利用了FFD法在双域实现的算法结构,明显减少了由于引入误差校正所带来的计算量.将该方法应用于修改后的三维French模型的地震正演问题,并将得到的叠后记录、单炮记录同全波有限差分法的模拟结果进行对比,结果证实了该方法对一次反射波具有较高的模拟精度,在内存需求和计算效率方面则具有更大的优势.     

Near-surface flow structure over wind-generated water waves,part I: wave-induced flow characteristics

We report on an experimental study conducted to investigate the influence of small-scale wind waves on the airflow structure in the immediate vicinity of the air–water interface. PIV technique was used to measure the two-dimensional velocity fields at wind speeds of 3.7 and 4.4 m?s^?1 and at a fetch of 2.1 m. The flow structure was analyzed as a function of wave phase. In the near-surface region, significant variations were observed in the flow structure over the waveform. The phase-averaged profiles of velocity, vorticity, and Reynolds stress showed different behavior on the windward and leeward sides of the wave in the near-surface region. The influence of wave-induced velocity was restricted within a distance of three significant wave heights from the surface, which also showed opposite trends on the windward and leeward sides of the crest. The results also show that the turbulent Reynolds stress mainly supports downward momentum transfer whereas the wave-induced Reynolds stress is responsible for the upward momentum transfer from wave to wind. In the immediate vicinity of the air–water interface, the momentum is transferred from waves to wind along the windward side, whereas, the momentum transfer is from wind to waves along the leeward side.     

A novel semi-analytical approach for non-uniform vegetated flows

In this paper a semi-analytical approach is proposed to understand the mechanism by which a non-uniform vegetated flowpasses over a finite thick soil layer covered with grass. The flow region is divided into three layers: a homogenous water layer, a mixed water-grass layer, and a finite thick soil layer (hereafter referred to as the water layer, the grass layer, and the soil layer). The flow of the water layer is governed by the Navier–Stokes equations. Both the grass and soil layers are regarded as porous media and the Biot’s theory of poroelasticity is applied to the porous medium flow. The semi-closed solutions are then obtained by the Runge–Kutta method. The drag force induced by the flow through the grass layer and the flow profiles of three patterns: submerged grass, emergent grass and mixed type are also discussed.