A generalized Ross method for two- and three-dimensional variably saturated flow

A numerical method has been proposed by Ross [Ross PJ. Modeling soil water and solute transport-fast, simplified numerical solutions. Agron J 2003; 95(6): 1352–1361.] to solve one-dimensional soil water movement problems. The Ross method is a noniterative numerical scheme, that can reduce computational time without sacrificing computational accuracy. The main aim of this study is to present a general form of the Ross method for two- and three-dimensional variably saturated flow. The established numerical model (R3D) is widely tested using five problems, in which the numerical solutions of R3D are compared with analytical solutions, laboratory data, and solutions from a traditional iterative numerical model. The comparison shows that R3D accommodates various hydraulic functions and boundary conditions. Results from R3D, which does not require iteration, are as accurate as results from iterative model. With the help of the primary variable switching technique, this model is unconditionally mass conservative, and computes infiltration into dry soil more efficiently. R3D is thus considered as an efficient tool for its high accuracy and efficiency for solving two- and three-dimensional variably saturated flow problems.     

A three dimensional model for water-sediment movement

A three-dimensional k-ε-Ap two-fluid turbulence model is proposed to study liquid-particle two-phase flow and bed deformation.By solving coupled liquid-phase and solid-phase governing equations in a finite-volume method,the model can calculate the movement of both water and sediment.The model was validated by water-sediment transport in a 180° channel bend with a movable bed.The validation concerns two-phase time-averaged velocities,bed deformation,water depth,depth-averaged streamwise velocity,cross-stream bed profiles,and two-phase secondary flow velocity vectors.The agreement between numerical results and experimental results was generally good.The comparisons of the numerical results of different models show that the three-dimensional k-ε-Ap two-fluid turbulence model has a relatively higher accuracy than one-fluid model.     

Irregular coastline and channeling effects in three-dimensional geomagnetic perturbation models

Two models, one with two small islands in a relatively narrow channel between two larger land masses and the other with an island near an irregular coast, are investigated with a view to assessing the importance of small-scale features. The perturbation of a uniform alternating geomagnetic field of various frequencies is studied by a numerical technique in which the inhomogeneous models are represented by cells of different conductivity within a three-dimensional mesh. The results are presented as contour plots of the amplitudes of the various field components over the surface of the conducting region, as well as by selected profiles of the field component amplitudes and phases. The channeling of currents around the higher resistivity island structures is apparent in the results. The effects of the small-scale structure of the coastline are pronounced in the model, and indicate that considerable care needs to be taken in selecting sites for experiments and in interpreting the results.     

A comparison of numerical,analogue model,and field-station vertical magnetic-fields for the Vancouver Island region

Vertical magnetic fields for a three-dimensional numerical model, for a laboratory-analogue model, and from field stations for the Vancouver Island region of British Columbia, Canada, are compared. The numerical results are obtained using a three-dimensional finite-difference numerical technique employing a 25 × 25 × 25 mesh of grid points for a simplified mathematical model of the Vancouver Island region. The calculations are carried out for a source frequency of 0.004 Hz. The analogue model results for four traverses over the Island model and the field station values (obtained from transfer function analysis) for ten locations are those discussed previously by Nienaber et al. (1979a, b). General agreement exists between the numerical, analogue, and field station data, and comparison of results between these methods is important in three-dimensional electromagnetic induction studies of complex geomagnetic induction problems.     

基于非结构网格求解三维D'Alembert介质中声波方程的并行加权Runge-Kutta间断有限元方法

间断有限元方法(Discontinuous Galerkin method,简称DGM)在求解地震波动方程时具有低数值频散、网格剖分灵活等优点,因此,为适应数值模拟对模拟精度和复杂地质结构的要求,本文提出一种新的加权Runge-Kutta间断有限元(weighted Runge-Kutta discontinuous ...     

Evaluation of sheet pile-ring countermeasure against liquefaction for oil tank site

The evaluation of a countermeasure against liquefaction which uses a sheet pilering for oil tank sites is presented. The simulation of earthquake responses observed at tank sites with and without sheet pile-ring is first performed to validate the three-dimensional finite element numerical model. Using the numerical model, liquefaction analysis is performed and the excess pore water pressure generated in the soil and the settlement of tank are investigated. The comparison of two- and three-dimensional models is also conducted to assess the applicability of two-dimensional analysis. The results show that the numerical model could simulate the observed earthquake responses of tank-ring-soil system, and that the excess pore water pressure and the settlement of the tank could be significantly reduced using a sheet pile-ring. The two-dimensional analysis proves to be capable of representing the main features of the dynamic response of the three-dimensional tank-ring-soil system.     

The perturbation of geomagnetic fields by two-dimensional and three-dimensional conductivity inhomogeneities

Summary A numerical method is used to calculate the geomagnetic fields associated with a three-dimensional conductivity anomaly. Fields associated with a two-dimensional model are also studied numerically for a range of frequencies and apparent resistivity curves for the two models are compared with that calculated for a layered earth. The apparent resistivity curves for both the three-dimensional model and the two-dimensional model differ considerably from the layered case, and it is evident that if a layered model is used for interpretation the results may be very misleading.     

三维井壁中子-中子测井数值模拟

应用多群P1近似和有限元方法对三维中子输运方程进行数值求解,并研究此方法在中子测井中的应用,实现了三维井壁中子-中子测井的数值正演研制了三维有限元中子测井软件包．应用它对江汉石油测井研究所的不同岩性的模型井进行了模拟计算,将计算结果同实验测量进行了比较,两者符合良好．用理论计算方法制作了各种环境校正图形曲线,计算精度令人满意．     

液化场地桥梁足尺桩抗震简化分析方法

采用国际VELACS项目中离心机试验标定的内华达砂的动力计算参数,建立液化场地足尺桩-土动力相互作用分析的三维有限元模型;获得不同幅值的正弦波作用下桩-土动力相互作用的p-y曲线,修正并发展一种可用于液化场地桩-土动力相互作用分析的宏单元模型,并基于非线性文克尔地基梁模型建立桥梁足尺桩抗震分析的数值模型与简化方法,通过有限元分析结果验证该简化方法的正确性。     

探地雷达三维高阶时域有限差分法模拟研究

探地雷达数值模拟中,时域有限差分法在时间和空间上一般采用二阶精度的中心差分近似(FDTD(2,2)),其形式简单,但数值色散误差较大,在复杂模型模拟时不能很好地反映模型的精细变化.高阶时域有限差分法能很好地改善数值色散带来的误差,提高模拟精度.本文基于三维高阶时域有限差分法的基本原理实现了探地雷达正演模拟,采用单轴各向异性完全匹配层(UPML)作为吸收边界条件,可以有效地吸收外向传播的电磁波,在大大地提高计算效率的同时,也能很好地改善边界的吸收效果.分析对比正演模拟结果,通过三维高阶时域有限差分正演能获得目标体准确电磁响应信息,并能很好的提高模拟精度.     

Influence of the turbulence closure scheme on the finite-element simulation of the upwelling in the wake of a shallow-water island

A three-dimensional finite-element model is used to investigate the tidal flow around Rattray Island, Great Barrier Reef, Australia. Field measurements and visual observations show both stable eddies developing at rising and falling tide in the wake of the island. The water turbidity suggests intense upwelling able to carry bed sediments upwards. Based on previous numerical studies, it remains unclear at this point whether the most intense upwelling occurs near the centre of the eddies or off the island's tips, closer to the island. All these studies resorted to a very simple turbulence closure, with a zero-equation model whereby the coefficient of vertical viscosity is computed via an algebraic expression. In this work, we aim at studying the influence of the turbulence closure on model results, with emphasis on the prediction of vertical motions. The Mellor and Yamada level 2.5 closure scheme is used and an increase in the intensity of vertical transport is observed. This increase is partly explained by the fact that the Mellor and Yamada model takes into account the hysteresis effect in the time variation of turbulence variables. The influence of the advection of turbulence variables is estimated to be negligible. By a better representation of transient coastal phenomena, the Mellor and Yamada level 2.5 turbulence closure improves the model to a significant degree.     

Barotropic wind-driven circulation patterns in a closed rectangular basin of variable depth influenced by a peninsula or an island

We study how a coastal obstruction (peninsula or coastal island) affects the three-dimensional barotropic currents in an oblong rectangular basin with variable bathymetry across the basin width. The transverse depth profile is asymmetric and the peninsula or island lies in the middle of the long side of the rectangle. A semi-spectral model for the Boussinesq-approximated shallow water equations, developed in Haidvogel et al. and altered for semi-implicit numerical integration in time in Wang and Hutter, is used to find the steady barotropic state circulation pattern to external winds. The structural (qualitative) rearrangements and quanti2tative features of the current pattern are studied under four principal wind directions and different lengths of the peninsula and its inclination relative to the shore. The essentially non-linear relationships of the water flux between the two sub-basins (formed by the obstructing peninsula) and the corresponding cross-sectional area left open are found and analysed. It is further analysed whether the depth-integrated model, usually adopted by others, is meaningful when applied to the water exchange problems. The flow through the channel narrowing is quantitatively estimated and compared with the three-dimensional results. The dynamics of the vortex structure and the identification of the up-welling/down-welling zones around the obstruction are discussed in detail. The influence of the transformation of the peninsula into a coastal island on the global basin circulation is considered as are the currents in the channel. The geometric and physical reasons for the anisotropy of the current structure which prevail through all obtained solutions are also discussed.Dedicated to Professor L.A. Mysak on the occasion of his sixtieth birthday.     

Validation and Verification of a Numerical Model for Tsunami Propagation and Runup

A robust numerical model to simulate propagation and runup of tsunami waves in the framework of non-linear shallow water theory is developed. The numerical code adopts a staggered leapfrog finite-difference scheme to solve the shallow water equations formulated for depth-averaged water fluxes in spherical coordinates. A temporal position of the shoreline is calculated using a free-surface moving boundary algorithm. For large scale problems, the developed algorithm is efficiently parallelized employing a domain decomposition technique. The developed numerical model is benchmarked in an exhaustive series of tests suggested by NOAA. We conducted analytical and laboratory benchmarking for the cases of solitary wave runup on simple beaches, runup of a solitary wave on a conically-shaped island, and the runup in the Monai Valley, Okushiri Island, Japan, during the 1993 Hokkaido-Nansei-Oki tsunami. In all conducted tests the calculated numerical solution is within an accuracy recommended by NOAA standards. We summarize results of numerical benchmarking of the model, its strengths and limits with regards to reproduction of fundamental features of coastal inundation, and also illustrate some possible improvements.     

Observations and simulations of an unsteady island wake in the Firth of Forth, Scotland

Beamer Rock, a 50-m-wide island in the Firth of Forth, produces a distinctive von Kármán vortex street wake, the characteristics of which depend on the speed and direction of the tidal flow. ADCP (acoustic Doppler current profiler), CTD (conductivity–temperature–depth) and aerial photograph data were collected from the region during flood and ebb tidal flow under neap and spring conditions. Good agreement was found between the observations and the results from a fixed-grid depth-averaged numerical tidal model. The island wake parameter correctly predicted the unsteady nature of the wake, and the Strouhal number (defined in terms of flow past a circular cylinder) was found to give excellent predictions of the wake wavelength when scaled on the island width. Contrary to published results, the study shows that it is possible to accurately simulate an unsteady island wake using a relatively coarse fixed-grid numerical model.Responsible Editor: Jens Kappenberg     

A semi-analytical boundary element method for scattering of waves in a half space

A boundary element method using finite strip discretization is proposed to investigate the three-dimensional scattering behaviour of waves in a half space. The scatterers examined are an irregular surface and a cavity in a half space. The numerical examples demonstrate the remarkably good accuracy of the results and validate the application of the present method to solve three-dimensional scattering problems.     

Lessons from and assessment of Boussinesq aquifer modeling of a large fluvial island in a dam-regulated river

The suitability of a numerical Boussinesq aquifer model for representing groundwater dynamics in a fluvial island surrounded by a regulated river is assessed and the model is used to compare exchange fluxes for varying configurations of island hydraulic conductivity (K) and diffusivity. The model results are qualitatively similar to field observations of the water table although there is obvious dissimilarity between modeled and observed heads suggesting that a Boussinesq aquifer model may not be the best option for representing the island. Nonetheless, the simulations show that pronounced ridges and valleys form in the water table and that their spatial configuration may change drastically with small variations in diffusivity. Stage fluctuations significantly increase exchange flux across the island relative to the case where stage is constant. The flux increases non-linearly when island K is low but then becomes quasi-linearly dependent on K with further increases in K. Regulated river stage fluctuations due to dams significantly affect surface water–groundwater interactions between a fluvial island and a river. This deserves further inquiry for both scientific and management reasons.     

三维复杂山谷地形SV波垂直输入地震反应分析

本文基于显式有限元法研究了地震波垂直入射时三维复杂山谷地形对地震地面运动的影响,在数值分析中应用了三维化二维的解法和黏弹性人工边界的处理方法,实现了地震波垂直输入下三维复杂场地地震动数值模拟,并验证了该方法的合理性.以四川桃坪地区一山谷地形作为研究对象,基于地表高程数据分别建立了二维和三维场地模型,对比研究表明:在复杂地形情况下考虑二、三维模型时具有明显差异,三维模型能更真实地反映地形变化对地震动的影响,复杂地形条件下有必要考虑三维实际场地模型.本文对边界自由场的处理方法也可用于处理三维复杂场地地震动斜入射问题,为三维复杂地形场地地震效应研究提供参考.     

A three dimensional k-ε-A_p model for water-sediment movement

A three-dimensional k-ε-Ap two-fluid turbulence model is proposed to study liquid-particle two-phase flow and bed deformation. By solving coupled liquid-phase and solid-phase governing equations in a finite-volume method, the model can calculate the movement of both water and sediment. The model was validated by water-sediment transport in a 180° channel bend with a movable bed. The validation concerns two-phase time-averaged velocities, bed deformation, water depth, depth-averaged streamwise velocity, cross-stream bed profiles, and two-phase secondary flow velocity vectors. The agreement between numerical results and experimental results was generally good. The comparisons of the numerical results of different models show that the three-dimensional k-ε-Ap two-fluid turbulence model has a relatively higher accuracy than one-fluid model.     

A numerical method for simulating non-Newtonian fluid flow and displacement in porous media

Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow.     

基于电场总场矢量有限元法的接地长导线源三维正演

电磁场数值模拟的背景场/异常场算法是三维正演的有效策略之一,优点为采用解析法计算电磁场背景场代替场源项、克服了场源奇异性,缺点为不适用于发射源布置于起伏地表或背景模型复杂的情形.总场算法是直接对电磁场总场开展数值模拟,其难点是有效加载场源、保证近区与过渡区数值解精度.本文以水平电偶源形式分段加载接地长导线源,并以电场总场Helmholtz方程为矢量有限元法控制方程,实现了基于非结构化四面体网格剖分的接地长导线源频率域电磁法三维正演.通过与均匀全空间中水平电偶源产生的电场解析解对比,验证了本文算法的正确性,并分析了四面体外接圆半径与其最短棱边的最大比值和四面体二面角最小值对数值解精度的影响规律.通过与块状高导体地电模型的积分方程法、有限体积法和基于磁矢量势Helmholtz方程的有限元法数值解对比,进一步验证了本文算法正确性,同时说明了非结构化四面体网格能够更加精细地剖分电性异常体,利于获得精确数值解.