Analysis of the pressure projection stabilization method for the Darcy and coupled Darcy–Stokes flows

In this paper, we systematically analyze the pressure projection stabilization method for the Darcy and coupled Darcy–Stokes flow problems in multiple dimensions. Stability results for this stabilization method are established. For the Darcy flow, optimal error estimates in the divergence norm for velocity and suboptimal error estimates in the $L^{2}$ -norm for pressure are obtained, and a superconvergence result for the pressure is derived; a local postprocessing scheme is constructed to generate optimal error estimates in the L ²-norm for pressure. For the coupled Darcy–Stokes flow, error estimates of optimal order are obtained in terms of the energy norm of velocity and pressure. Numerical results are presented to check the theory developed.     

原位“Darcy实验”方法研究与实践

在室内Darcy实验原理和装置的基础上,设计了一套原位“Darcy实验”装置,原位试验条件满足Darcy定律的假定条件,能够应用Darcy定律确定包气带浅表层土的渗透系数.与室内“Darcy实验”相比,原位“Darcy实验”的测试结果更能准确地反映结构性土野外状态下的渗透性能.与其它原位试验相比,该方法在获取渗透系数方面具有试验装置简单、操作方便、观测数据直观的优点.应用该方法在中国西北部半干旱的黄土台塬开展了3组测试,成功地求取了区内包气带浅表层饱和黄土的垂向渗透系数,并将测试结果与双环试验、室内渗透试验、抽水试验及颗粒分析方法求得的渗透系数结果进行对比分析,发现应用原位“Darcy实验”求取的渗透系数更能准确地反映包气带浅表层土的渗透性能.同时,总结和探讨了一套原位“Darcy实验”的技术方法.     

On classical iterative subdomain methods for the Stokes–Darcy problem

Within classical iterative subdomain methods, the problems in the subdomains are solved alternately by only using data on the interface provided from the other subdomains. Methods of this type for the Stokes–Darcy problem that use Robin boundary conditions on the interface are reviewed. Their common underlying structure and their main differences are identified. In particular, it is clarified that there are different updating strategies for the interface conditions. For small values of fluid viscosity and hydraulic permeability, which are relevant in applications from geosciences, it is shown in numerical studies that only one of these updating strategies leads to an efficient numerical method, if it is used with appropriate parameters in the Robin conditions.     

考虑粘性土体低速非Darcy渗流地面沉降模拟的探讨

过度抽汲地下水引发的地面沉降是全球广泛关注的地质环境问题。对其进行数值模拟是实现地面沉降灾害科学管理的最有效手段。水流模型是地面沉降模型的必要组成部分,对其刻画得准确与否将影响沉降模拟的准确度。本文首先综述了低渗透性粘性土体中的低速非线性Darcy渗流规律,而后从地面沉降发生的地质背景分析出发,论证了低速非线性Darcy渗流对地面沉降模拟的作用,并讨论了当前地面沉降模拟中水流模型刻画的不足之处。最后提出了如何在地面沉降模拟中考虑低速非Darcy渗流的4个关键性科学问题,对该问题的探讨有助于提高地面沉降模拟的准确性。     

考虑非Darcy渗流时循环荷载下饱和黏土一维固结分析

考虑到土体处于超固结状态下的压缩性一般要比正常固结状态下的低,引入描述非Darcy渗流的Hansbo方程,修正了Terzaghi饱和黏土一维固结方程,并将其推广到低频循环荷载作用的情况。采用有限体积法对该方程进行了求解,并讨论了非Darcy渗流参数、循环荷载周期以及超固结状态下土体压缩性对固结进程的影响。计算结果表明,在矩形波载作用下,按孔压定义和按变形定义的固结度都随时间增长而震荡增加,且按孔压定义的固结度的震荡幅度明显大于按变形定义的固结度。另外,非Darcy渗流减缓了地基的沉降速率,且循环荷载周期越短,或超固结状态下压缩性越高,地基的沉降速率就越慢。     

碎(块)石路堤孔隙空气对流运动的Darcy定律适用性

针对青藏高原多年冻土区路基工程中采用的碎石路堤地温调控技术,分析了碎石层孔隙空气对流运动符合Darcy定律的适用范围及其可能偏离Darcy定律的非线性效应,并给出了考虑非线性效应的Darcy定律修正方程.同时,讨论了适合于路堤碎石层的空气渗透系数及其表征空气流动非线性效应的Ergun常数的估算公式.     

A discretization and multigrid solver for a Darcy–Stokes system of three dimensional vuggy porous media

We develop a finite element discretization and multigrid solver for a Darcy–Stokes system of three-dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low-order mixed finite elements in the Darcy and Stokes domains and special transition elements near the Darcy–Stokes interface to allow for tangential discontinuities implied by the Beavers–Joseph boundary condition. We design a multigrid method to solve the resulting saddle point linear system. The intertwining of the Darcy and Stokes subdomains makes the resulting matrix highly ill-conditioned. The velocity field is very irregular, and its discontinuous tangential component at the Darcy–Stokes interface makes it difficult to define intergrid transfer operators. Our definition is based on mass conservation and the analysis of the orders of magnitude of the solution. The coarser grid equations are defined using the Galerkin method. A new smoother of Uzawa type is developed based on taking an optimal step in a good search direction. Our algorithm has a measured convergence factor independent of the size of the system, at least when there are no disconnected vugs. We study the macroscopic effective permeability of a vuggy medium, showing that the influence of vug orientation; shape; and, most importantly, interconnectivity determine the macroscopic flow properties of the medium. This work was supported by the U.S. National Science Foundation under grants DMS-0074310 and DMS-0417431.     

等深流与等深流沉积

综述了国内外学者对等深流及其沉积物的研究现状。全面介绍了等深流的概念、“深海风暴”的成因、现代海洋等深流的沉积作用、等深流沉积物的特征、等深积岩的识别以及研究意义和存在问题。     

Multiple flow and support mechanisms and the development of inverse grading in a subaquatic glacigenic debris flow

Subaquatic glacigenic debris flows of Late Wisconsinan age occur as lobes within an ice-marginal glaciomarine lithofacies at Victoria, British Columbia. Flow was initiated by release of supraglacial debris during an interval of glacial ablation prior to advance and deposition of lodgement till. Many of the lobes developed a common morphology during deposition, consisting of an outer layer surrounding an inner core of rafted material. In the largest lobe reworking of the sediment during flow produced improved sorting, a coarsening of mean grain size, and a shift in skewness toward the negative. This occurred simultaneously within the core and outer layer as a result of different transformations in mechanisms of flow and support. Normal grading, produced in the outer layer, was conveyed around the nose and buried in an inverse position along the base of the flow. These data enable us to present a model that may be applicable to similar flows elsewhere. The flow studied demonstrates that transformations between flow types and sediment support mechanisms can occur simultaneously and serially in subaquatic debris flows.     

Properties of debris flow deposits and source materials compared: implications for debris flow characterization

In the Alps, debris flow deposits generally contain <5% clay‐size particles, and the role of the surface‐charged <2 μm particles is often neglected, although these particles may have a significant impact on the rheological properties of the interstitial fluid. The objective of this study was to compare debris flow deposits and parent materials from two neighbouring catchments of the Swiss Alps, with special emphasis on the colloidal constituents. The catchments are small in area (4 km²), 2·5 km long, similar in morphology, but different in geology. The average slopes are 35–40%. The catchments were monitored for debris flow events and mapped for surface aspect and erosion activity. Debris flow deposits and parent materials were sampled, the clay and silt fractions extracted and the bulk density, <2 mm fraction bulk density, particle size distribution, chemical composition, cation exchange capacity (CEC) and mineralogy analysed. The results show that the deposits are similar to the parent screes in terms of chemical composition, but differ in terms of: (i) particle size distribution; and (ii) mineralogy, reactivity and density of the <2 mm fraction. In this fraction, compared with the parent materials the deposits show dense materials enriched in coarse monocrystalline particles, of which the smallest and more reactive particles were leached. The results suggest that deposit samples should not be considered as representative of source or flow materials, particularly with respect to their physical properties.     

坡面流层流区动力学特性

为完善坡面水流的基础理论研究,基于定床水槽试验,以甘油溶液为试验流体,采用超声波测量技术,进行了4种粗糙度、5种坡度和13种单宽流量条件下的组合试验,研究了坡面流层流区的动力学特性及滚波特征。研究结果表明:在雷诺数为8~160的范围内,流态指数在理论值0.33附近波动,且随粗糙度的增大呈现先增大后减小的变化趋势,在粗糙度为0.10 mm附近达到峰值;阻力系数受坡度和粗糙度影响显著,可较好地由坡度、粗糙度和雷诺数的关系式表示;随着雷诺数的增大,滚波波速和波峰均呈幂函数形式递增,滚波周期大小无明显变化;坡度的增大会使层流失稳临界单宽流量减小,粗糙度的增大会使临界弗劳德数的均值减小。     

明渠恒定紊流的总流控制方程与能量损失特性

为进一步深化对明渠总流控制方程的认识,探究总流能量损失的构成与分布特点,通过理论分析,在黏性流体力学理论的框架下构建了描述明渠恒定紊流总体特性的总流积分模型与总流微分模型的控制方程,其模型参数能直接通过流动统计特征量在过流断面上的分布来获取,由此实现明渠流的流场特性描述与总流描述的统一,并得到了总流能量损失的显示表达式。同时指出,总流能量损失由黏性耗散与维持紊动两部分构成,在矩形明渠恒定均匀流紊流的分类能量损失构成中,壁面上以黏性耗散部分为主,维持紊动部分的能量损失密度随着离开壁面距离的增加而快速增加,且随着雷诺数的增大,其增加速度也越快。     

明渠恒定紊流的总流控制方程与能量损失特性

为进一步深化对明渠总流控制方程的认识,探究总流能量损失的构成与分布特点,通过理论分析,在黏性流体力学理论的框架下构建了描述明渠恒定紊流总体特性的总流积分模型与总流微分模型的控制方程,其模型参数能直接通过流动统计特征量在过流断面上的分布来获取,由此实现明渠流的流场特性描述与总流描述的统一,并得到了总流能量损失的显示表达式。同时指出,总流能量损失由黏性耗散与维持紊动两部分构成,在矩形明渠恒定均匀流紊流的分类能量损失构成中,壁面上以黏性耗散部分为主,维持紊动部分的能量损失密度随着离开壁面距离的增加而快速增加,且随着雷诺数的增大,其增加速度也越快。     

冲洪积平原渗流和管流耦合的辐射井结构

利用新疆阿克苏台兰河流域冲洪积平原区非稳定流抽水试验资料,以辐射井为研究对象,结合辐射管内的水头损失及流态,建立粗颗粒潜水含水层渗流和水平管流耦合的地下水流数值模型。利用数值模型,分析在粗颗粒含水层中辐射管不同根数、不同长度、等效渗透系数、辐射井的井径以及不同含水层的渗透系数、不同降深对辐射井出水量的影响,并且根据各参数的相互关系,提出冲洪积平原辐射井的出水量的经验公式。为优化设计辐射井结构及辐射井布置提供依据,对台兰河地下水库的建设及后期运行管理提供了技术支撑。     

Preferential flow,diffuse flow,and perching in an interbedded fractured-rock unsaturated zone

Layers of strong geologic contrast within the unsaturated zone can control recharge and contaminant transport to underlying aquifers. Slow diffuse flow in certain geologic layers, and rapid preferential flow in others, complicates the prediction of vertical and lateral fluxes. A simple model is presented, designed to use limited geological site information to predict these critical subsurface processes in response to a sustained infiltration source. The model is developed and tested using site-specific information from the Idaho National Laboratory in the Eastern Snake River Plain (ESRP), USA, where there are natural and anthropogenic sources of high-volume infiltration from floods, spills, leaks, wastewater disposal, retention ponds, and hydrologic field experiments. The thick unsaturated zone overlying the ESRP aquifer is a good example of a sharply stratified unsaturated zone. Sedimentary interbeds are interspersed between massive and fractured basalt units. The combination of surficial sediments, basalts, and interbeds determines the water fluxes through the variably saturated subsurface. Interbeds are generally less conductive, sometimes causing perched water to collect above them. The model successfully predicts the volume and extent of perching and approximates vertical travel times during events that generate high fluxes from the land surface. These developments are applicable to sites having a thick, geologically complex unsaturated zone of substantial thickness in which preferential and diffuse flow, and perching of percolated water, are important to contaminant transport or aquifer recharge.     

过渡型流体转换对洪水型重力流沉积研究的启示及地质意义

洪水型重力流是重力流沉积学的研究热点,以往研究认为洪水型重力流具有紊流支撑的流体性质,对于其流体性质转化及其沉积记录的识别不够深入。近年研究揭示重力流沉积过程中可形成多种过渡型流体,具有特殊流体转换机制和沉积特征。通过调研国内外最新文献,系统介绍了过渡型流体基本特征、沉积机制方面的研究进展,并讨论了其对洪水型重力流沉积研究的启示及地质意义。研究结果表明：在少量黏土矿物影响下,沉积物重力流流体的性质即可由紊流向层流转化,形成特殊的过渡型流体。转化过程主要取决于黏土矿物含量和类型控制的流体内聚力和流速控制的紊流应力二者之间的相互作用。过渡型流体可以产生大型流水沙纹（large current ripple）、砂质纹层—泥质纹层间互形成的低幅度沙波（low amplitude bed wave）等独特的底床类型。尽管实验研究揭示了过渡型流体可能形成的沉积底床特征,针对洪水型重力流沉积记录中过渡型流体的解释仍十分缺乏,尤其是过渡型流体转换机制及其沉积响应仍亟待深入探索。过渡型流体的沉积底形是研究洪水型重力流沉积动力机制的重要载体,可为深入理解洪水型重力流沉积过程提供新视角,同时可能具有更广泛的沉积学研究价值。     

过渡型流体转换对洪水型重力流沉积研究的启示及地质意义

洪水型重力流是重力流沉积学的研究热点,以往研究认为洪水型重力流具有紊流支撑的流体性质,对于其流体性质转化及其沉积记录的识别不够深入。近年研究揭示重力流沉积过程中可形成多种过渡型流体,具有特殊流体转换机制和沉积特征。通过调研国内外最新文献,系统介绍了过渡型流体基本特征、沉积机制方面的研究进展,并讨论了其对洪水型重力流沉积研究的启示及地质意义。研究结果表明：在少量黏土矿物影响下,沉积物重力流流体的性质即可由紊流向层流转化,形成特殊的过渡型流体。转化过程主要取决于黏土矿物含量和类型控制的流体内聚力和流速控制的紊流应力二者之间的相互作用。过渡型流体可以产生大型流水沙纹(large current ripple)、砂质纹层—泥质纹层间互形成的低幅度沙波(low amplitude bed wave)等独特的底床类型。尽管实验研究揭示了过渡型流体可能形成的沉积底床特征,针对洪水型重力流沉积记录中过渡型流体的解释仍十分缺乏,尤其是过渡型流体转换机制及其沉积响应仍亟待深入探索。过渡型流体的沉积底形是研究洪水型重力流沉积动力机制的重要载体,可为深入理解洪水型重力流沉积过程提供新视角,同时可能具有更广泛的...     

Plastic flow and state-dilatancy for geomaterials

In this paper, the stress-dilatancy hypothesis is revisited and a stress-dilatancy framework is established such that it can be compatibly used for different yield functions. The influence of density–pressure and other state variables are systematically accommodated. The framework is further evaluated by obtaining and extending some flow rules for the Mohr–Coulomb criterion and novel stress-dilatancy formalism for the Hoek–Brown criterion.