Local problem-based <Emphasis Type="Italic">a posteriori</Emphasis> error estimators for discontinuous Galerkin approximations of reactive transport

We consider adaptive discontinuous Galerkin (DG) methods for solving reactive transport problems in porous media. To guide anisotropic and dynamic mesh adaptation, a posteriori error estimators based on solving local problems are established. These error estimators are efficient to compute and effective to capture local phenomena, and they apply to all the four primal DG schemes, namely, symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and the Oden–Babuška-Baumann version of DG. Numerical results are provided to illustrate the effectiveness of the proposed error estimators.     

A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure

In this paper, we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential/capillary potential formulation of the two-phase flow system. After discretizing in time with diagonally implicit Runge-Kutta schemes, the resulting systems of nonlinear algebraic equations are solved with Newton’s method and the arising systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. The new scheme is investigated for various test problems from the literature and is also compared to a cell-centered finite volume scheme in terms of accuracy and time to solution. We find that the method is accurate, robust, and efficient. In particular, no postprocessing of the DG velocity field is necessary in contrast to results reported by several authors for decoupled schemes. Moreover, the solver scales well in parallel and three-dimensional problems with up to nearly 100 million degrees of freedom per time step have been computed on 1,000 processors.     

Enhanced velocity mixed finite element methods for modeling coupled flow and transport on non-matching multiblock grids

The enhanced velocity mixed finite element method, due to Wheeler et al. (Comput Geosci 6(3–4):315–332, 2002), is analyzed and extended to the problem of modeling slightly compressible flow coupled to the transport of chemical species through porous media, on non-matching multiblock grids. Applications include modeling bio-remediation of heavy oil spills and many other subsurface hazardous wastes, angiogenesis in transition of tumors from dormant to malignant states, transport of contaminants in ground water flow, and acid injection from well bores to increase permeability of surrounding rock. The analysis and numerical examples presented here demonstrate convergence and computational efficiency of this method.     

Approximation of the Velocity by Coupling Discontinuous Galerkin and Mixed Finite Element Methods for Flow Problems

In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart–Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart–Thomas space of polynomials of degree k?1.     

基于结构网格的溃坝水流数值模拟

针对溃坝水流数值模拟面临的复杂地形和不规则边界等问题,基于结构网格建立了适应复杂地形和不规则边界的溃坝水流数值模拟有限体积模型（HydroM2D）。模型基于具有守恒特性的二维浅水方程,利用HLLC格式的近似Riemann解计算网格界面通量,利用MUSCL-Hancock法不断向前积分,使模型在时空上具有二阶精度;对源项进行离散处理确保模型的稳定性;模型引入有效干湿边界和不规则地形边界处理方法,准确模拟了干湿单元的动态交替和复杂边界上的水流特性。最后分别利用水槽试验、物理模型和实际算例对模型进行验证。结果表明,该模型对不同情景下的溃坝洪水模拟结果和实测资料以及现有模型模拟结果具有较高的一致性,模拟精度较高,稳定性较好,具有推广应用价值。     

A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations

In this paper, we study the properties of approximate solutions to a doubly nonlinear and degenerate diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW), using a numerical approach based on the Galerkin finite element method. This equation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases the porous medium equation and the p-Laplacian. Diverse numerical schemes have been implemented to approximately solve the DSW equation and have been successfully applied as suitable models to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis has been carried out in order to study the properties of approximate solutions. In this study, we propose a numerical approach as a means to understand some properties of solutions to the DSW equation and, thus, to provide conditions for which the use of the DSW equation may be inappropriate from both the physical and the mathematical points of view, within the context of shallow water modeling. For analysis purposes, we propose a numerical method based on the Galerkin method and we obtain a priori error estimates between the approximate solutions and weak solutions to the DSW equation under physically consistent assumptions. We also present some numerical experiments that provide relevant information about the accuracy of the proposed numerical method to solve the DSW equation and the applicability of the DSW equation as a model to simulate observed quantities in an experimental setting.     

A semi‐analytical solution of surface flow and subsurface flow on a slope land under a uniform rainfall excess

A new approach is proposed to analyze the surface flow and subsurface flow passing over a pervious ground under a uniform rainfall excess. The flow field is divided into two regions that are called water layer and soil layer. To figure out the hydraulic behavior of overland flow on an inclined plane under a rainfall event, the simplified Navier–Stokes equations are employed for the surface water flow, and the flow inside the soil layer is porous media flow, which is governed by Biot's (1956, 1962) theory of poroelasticity. The velocity distribution of overland flow is nonzero at the ground surface. The relation between water depth and slope length was developed first. The profile of surface water flow was then found backwards from the downstream end of the flow section by the Runge–Kutta method. After that, the flow velocity and flow discharge of each layer could also be obtained via the water depth. Finally, the variation of fluid shear stress inside the soil layer is also discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Runge-Kutta间断有限元格式在一维浅水方程中的应用

针对一维浅水方程组建立了考虑源项离散的Runge-Kutta间断有限元格式,该格式具有通量与源项的和谐性,可以用于求解任意非棱柱体明渠浅水流动问题。所建立的数值模式分别应用于复杂地形下非棱柱体明渠跨临界流浅水流动算例和水跃问题,模拟结果表明,数值解与解析解以及实测值吻合良好,数值格式具有捕捉间断问题中锐利波形的能力。     

斜坡降雨入渗在Flac中模拟

为了简化分析,在模拟斜坡降雨入渗暂态渗流时,通常没有考虑入渗和产流的耦合过程,通过施加流量边界或零水头边界进行地下水渗流计算,通过在FALC中利用内嵌的fish语言,考虑地表径流和地下渗流的耦合以及雨向影响下斜坡降雨入渗过程,并通过算例分析了考虑和不考虑耦合、对斜坡孔隙水压力分布以及考虑各种雨向作用下对坡面积水深度的影响。     

Some aspects of head‐variance evaluation

We compare two methods of evaluating head covariance for two‐dimensional steady‐state flow in mildly heterogeneous bounded rectangular aquifers. The quasi‐analytical approach, widely used in stochastic subsurface hydrology, is based on the Green's function representation, and involves numerical four‐fold integration. We compare this approach with a numerical solution of the two‐dimensional boundary‐value problem for head covariance. We show that the finite differences integration of this problem is computationally less expensive than numerical four‐fold integration of slowly‐convergent infinite series. This revised version was published online in July 2006 with corrections to the Cover Date.     

路基下伏地质缺陷弹性波数值模拟

针对我国西部黄土地区特殊的地形地貌、近地表条件和地下浅层目标体,开展了路基下伏地质缺陷地震探测技术的应用研究。为检验不同地震方法的探测能力,设计了一个综合地质地球物理模型,包含凹陷、断层、地裂缝、地下低速体、软弱夹层及滑坡等典型地质缺陷,利用有限差分波场模拟,计算出多分量反射地震记录和面波地震记录,分别进行了反射波成像和高阶面波反演横波速度成像。数值模拟结果表明,反射波成像和高阶面波反演横波速度成像技术对真实模型中的凹陷、断层、浅层低速体、软弱夹层及滑坡等主要地质缺陷均能清晰成像,验证了地震方法探测路基下伏地质缺陷的可行性。数值计算结果表明,不同的地球物理探测方法对地质缺陷的探测效果和适用范围不同。     

基于流动电位正演模型的非饱和带水流过程监测

为了获取非饱和带水流过程的信息,借助流动电位正演模型,通过数值实验探讨非降雨和降雨两种条件下非饱和带流动电位和水流过程的关系,然后用南京中山植物园试验场地野外观测的流动电位和张力数据加以对比和验证。野外试验表明:流动电位可以有效地反映非饱和带水流过程。在夏季无降雨入渗的条件下,日周期变化的地表地下温度差导致水分的运动,流动电位准确地指示了非饱和带含水量和毛细压力的变化情况,从而指示出了水分运移的方向;在夏季有降雨入渗的条件下,降雨锋面推进之处,含水量和流动电位同时有明显的响应,进而根据不同位置的流动电位对降雨入渗响应的时刻差,直接求出入渗锋面的推进速度。     

地下水模型的Neumann展开Monte-Carlo随机有限元法

讨论了求解地下水模型(水流模型和水质模型)的Neumann展开Monte-Carlo随机有限元法。从基本的随机变量入手,避免了过程中随机变量的增多问题,给出结点水头(浓度)的均值、方差和水头在某区间的概率计算方法;改进了矩阵求逆的效率,对输入随机变量较多、随机变量变异较大的非稳定地下水问题特别有效。同时选取二维承压地下水水流问题(有解析解)作为例子,进行了随机数值模拟实验。      

Streamline method for resolving sharp fronts for complex two-phase flow in porous media

In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully implicit finite-volume methods are provided.     

间断水波在梯级水库中的传播

基于矢通量分裂得到了一维浅水方程组的隐式守恒有限差分格式,并对有底坡、有摩阻的梯级水库同时溃坝和相继溃坝的溃坝波传播进行了数值模拟。对数值结果作了分析。结果合理,方法有效可行。     

Liquefaction Hazard Assessment of Earth Quake Prone Area: a Study Based on Shear Wave Velocity by Multichannel Analysis of Surface Waves (MASW)

The shear wave velocity (V_S) profile based on the dispersive characteristics of fundamental mode of Rayleigh type surface waves indicate underground stiffness change with depth as well as near surface stiffness. The most important utility of shear wave velocity (V_S) is to estimate the liquefaction hazard potential of an area particularly in seismically active region. Rayleigh type surface waves were utilized to estimate the velocity (V_S) of shallow subsurface covering a depth range of 30–50 m employing multichannel analysis of surface waves. The liquefaction hazard map predicts an approximate percentage of an area that will have surface manifestation of liquefaction during an earth quake. The surface wave data acquired in an earth quake prone region of Jabalpur (Seismic zone III), India, yields a velocity (V_S) range of 200–750 m/s corresponding to the subsurface depth of 30–35 m. The results were analyzed for possible liquefaction hazard in the study area and presented here besides the N values.     

岩体裂隙网络渗流变水温影响分析

考虑岩体裂隙渗流变水温影响,推导单裂隙变水温水流近似解析解和有限元解,在此基础上分别建立裂隙二维网络变水温渗流数值求解方程,分别对应裂隙网络变水温渗流分析的近似解析法和子结构法。分析变温水流运动规律发现：（1）单裂隙内水流水头与水力坡降成非线性关系,当水流由高温区向低温区流动时,水头分布曲线为凸曲线,此时按线性渗流简化水头整体偏小;当由低温区向高温区流动时,水头分布曲线为凹曲线,此时按线性渗流简化水头整体偏大。（2）单裂隙内,高水温处水力坡降小,低水温处水力坡降大;裂隙平均水温越高,流速越快;裂隙网络内存在与裂隙宽度相似的温度偏流效应,即交叉节点水流有偏向水流温度高的裂隙流动的趋势。在温度较高和温度梯度较大的区域,应该考虑水流温度变化对渗流场的影响。     

Comparison of Numerical Formulations for Two-phase Flow in Porous Media

Numerical approximation based on different forms of the governing partial differential equation can lead to significantly different results for two-phase flow in porous media. Selecting the proper primary variables is a critical step in efficiently modeling the highly nonlinear problem of multiphase subsurface flow. A comparison of various forms of numerical approximations for two-phase flow equations is performed in this work. Three forms of equations including the pressure-based, mixed pressure–saturation and modified pressure–saturation are examined. Each of these three highly nonlinear formulations is approximated using finite difference method and is linearized using both Picard and Newton–Raphson linearization approaches. Model simulations for several test cases demonstrate that pressure based form provides better results compared to the pressure–saturation approach in terms of CPU_time and the number of iterations. The modification of pressure–saturation approach improves accuracy of the results. Also it is shown that the Newton–Raphson linearization approach performed better in comparison to the Picard iteration linearization approach with the exception for in the pressure–saturation form.     

Neural network modeling applications in active slope stability problems

A back propagation artificial neural network approach is applied to three common challenges in engineering geology: (1) characterization of subsurface geometry/position of the slip (or failure surface) of active landslides, (2) assessment of slope displacements based on ground water elevation and climate, and (3) assessment of groundwater elevations based on climate data. Series of neural network models are trained, validated, and applied to a landslide study along Lake Michigan and cases from the literature. The subsurface characterization results are also compared to a limit equilibrium circular failure surface search with specific adopted boundary conditions. It is determined that the neural network models predict slip surfaces better than the limit equilibrium slip surface search using the most conservative criteria. Displacements and groundwater elevations are also predicted fairly well, in real time. The models’ ability to predict displacements and groundwater elevations provides a foundational framework for building future warning systems with additional inputs.     

季节冻土区埋地管道水温的变化规律及其影响因素分析

埋地管道是减少寒冷地区冬季冻害的常用铺设方式,深入认识埋地管道的水温变化规律可以为减小管道埋设深度、降低管道冻害提供理论依据,对当前季节冻土区农牧民集中式供水工程的推进具有指导意义. 采用仿三维数值方法建立了管道水温的计算模型,讨论了含水量、地表温度、管道埋深等6个主要因素对埋地管道最不利水温的影响. 分析结果表明,无论上述因素如何变化,管道最不利水温均随输送距离的增加而下降. 首先,随着含水量的增加、地表温度的升高以及管道埋深的加深,管道的降温速率不断减小并具有先快后慢的特点;其次,随着管径的减小、流速的降低,管道降温速率增大,且降温速率和流速之间具有近似的倒数关系. 另外,随着入口温度的升高,管道降温速率将呈指数形式不断增加.