Two‐phase flows in karstic geometry

Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil, and gas), and cloud and fog (water vapor, water, and air). Multiphase flows also play an important role in many engineering and environmental science applications. In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits, and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. Despite the importance of the subject, little work has been performed on multiphase flows in karstic geometry. In this paper, we present a family of phase–field (diffusive interface) models for two‐phase flow in karstic geometry. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws. A uniquely solvable numerical scheme that preserves the associated energy law is presented as well. Copyright © 2013 John Wiley & Sons, Ltd.     

Lie rings defined by the root system and family of additive subgroups of the initial ring

The paper surveys mathematical models of magma flow in a volcanic conduit in the case of extrusive (nonexplosive) eruption that were developed in the group of dynamic volcanology at the Institute of Mechanics, Moscow State University, under the supervision of Professor A.A. Barmin. In the quasi-one-dimensional and two-dimensional formulations, the effect of crystallization, heat exchange, and viscous dissipation on the relationship between the magma discharge rate and the pressure difference between the magma chamber and atmosphere is analyzed. It is shown that there exist several steady-state solutions of the boundary value problem that differ in discharge rates by orders of magnitude. A transition between steadystate solutions may lead to cyclic variations in the magma discharge rate. Limitations of the hydraulic approach, which is based on the parameters averaged over the cross-section of a volcanic conduit, are revealed.     

Modeling of shallow aquifers in interaction with overland water

In this paper, we present a new class of efficient models for water flow in shallow unconfined aquifers, providing an alternative to the classical but less tractable 3d-Richards model. Its derivation is guided by two objectives: to obtain a model that has low computational cost and yields relevant results on every time scale.Thus, we keep track of two types of flow that occur in such a context and are dominant when the ratio of thickness to longitudinal length is small: the first is dominant on a small time scale and is described by a vertical 1d-Richards problem; the second corresponds to a large time scale, when the evolution of the hydraulic head becomes independent of the vertical variable. These two types of flow are appropriately modeled by a one-dimensional and two-dimensional system of PDE boundary value problems, respectively. They are coupled at an artificial level below which the Dupuit hypothesis holds true (i.e., the vertical flow is instantaneous) so that the global model is mass conservative. Tuning the artificial level, which can even depend on an unknown of the problem, we obtain the new class of models. Using asymptotic expansions, we prove that the 3d-Richards model and each model in the class behave identically on every considered time scale (short, intermediate, and large) in thin aquifers. The results are illustrated by numerical simulations, and it is demonstrated that they fit well with those obtained by the original 3d-Richards model even in non-thin aquifers.     

Analysis and finite element approximation of a coupled,continuum pipe‐flow/Darcy model for flow in porous media with embedded conduits

We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. The mathematical well‐posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two‐dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1242–1252, 2011     

Finite volume element approximation of the coupled continuum pipe‐flow/Darcy model for flows in karst aquifers

A finite volume element method is applied to approximate the continuum pipe‐flow/Darcy problem, which models the coupled conduit flow and porous media flow in Karst aquifers. A decoupled scheme is proposed for solving the coupled discretization problem. Optimal error estimates in L² norm and H¹ norm are given in this article. Some numerical examples are presented to verify the theoretical results and demonstrate the effectiveness of the decoupling approach. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 376–392, 2014     

An efficient method for solving an inverse problem for the Richards equation

A parameter identification problem for the hydraulic properties of porous media is considered. Numerically, this inverse problem is solved by minimizing an output least-squares functional. The unknown hydraulic properties which are nonlinear coefficients of a partial differential equation are approximated by spline functions. The identification is embedded into a multi-level algorithm and coupled with a linear sensitivity analysis to describe the ill-posedness of the inverse problem.     

Transient entropy generation analysis of vortex liquid isolated by hollow heated cylinder

The total transient entropy generation of a system that consists of a liquid vortex within a hollow cylinder as a heat source is investigated in this article. The hollow cylinder insulates the liquid vortex, and generates an air vacuum above the vortex which raises its level within the cylinder. The liquid vortex, at a volume of 20% and 60%, partially fills the hollow cylinder. In both cases, the heat transfer was partially established between the inner surface of the hollow cylinder and the vortex liquid. This analysis focused on the transient exchange of entropy generation between the cylinder and fluid. The heat exchange between the hollow heated cylinder and the fluids takes 15 s. The analysis of entropy generated includes only thermal irreversibility of this system; hydraulic irreversibility is neglected.     

Emergence and collapse of money through reciprocity

In this paper we discuss that monetary exchange emerges in a reciprocal system which consists of donations and returns. Agents reciprocate goods alternately without bilateral agreement in the system, that is constructed not from the viewpoint of the recipient, but from the one of the reciprocator. Moreover, reciprocity is regarded as interaction with incomplete identification consisting of the alternate procedure of constructing a map from coarse-grained data by a contraction mapping and of applying the map to fine-grained data. We show that reciprocity gives rise to the monetary exchange which implies globality without the concept of metric space or global semantics. It seems that interaction with incomplete identification does not carry the notion of globality. On the contrary, in our model globality paradoxically occurs from the accumulation of indefinite incomplete identification.     

An analytical model for carrier-facilitated solute transport in weakly heterogeneous porous media

Carrier-facilitated solute transport in heterogeneous aquifers is studied within a Lagrangian framework. Dissolved solutes and carriers are advected by steady random groundwater flow, which is modeled by Darcy's law with uncertain hydraulic conductivity that is treated as a stationary random space function. We derive general expressions for the spatial moments of the dissolved concentration and the concentration associated with the carrier phase. In order to reduce the computational effort, we use previously derived solutions for the flow field. This enables us to obtain closed-form solutions for the spatial moments of the two concentration fields. The mass and center of gravity of the two propagating plumes depend only on the mean velocity field and chemical/degradation processes. The higher (second and third) moments are affected by the coupling between reactions (sorption/desorption and degradation) among the three phases (i.e., dissolved, carrier and sorbed concentrations) and the aquifer’s heterogeneity. We investigate the potentially enhancing effect of carriers by comparing spatial moments of the two propagating plumes. The forward/backward mass transfer rates between the liquid and carrier phases, and the degradation coefficients are identified as critical parameters. The carrier's role is most prominent when detachment from carrier sites is slow, provided that degradation on the carriers is smaller than that in the liquid phase.     

基于混合C藤Copula的我国一篮子货币汇率相依结构研究

利用C藤模型及人民币对欧元、澳元、日元、美元、卢布、加元、英镑、林吉特的汇率数据,构建了我国一篮子货币汇率的C藤结构,用来描述各汇率间的相依结构.结果表明,人民币对欧元的汇率是中心汇率,也就是说,一篮子货币汇率的决定很大程度上依赖于人民币对欧元的汇率.人民币对欧元汇率与人民币对其它国家货币汇率的相依程度反映了不同市场的强弱和市场间进出口贸易额的大小.进一步,混合C藤中各根节点的排序一定程度上反映了货币篮子中各国的经济实力及与我国的贸易额大小.     

多偏移距电磁波数值成像的高阶FDTD法研究

数值模拟是数据处理和反演解释的重要环节,为提高高频电磁波层析成像技术在工程勘察中的解译准确性,采用高阶时间域有限差分法(FDTD(2阶时间精度,4阶空间精度))模拟电磁波在溶洞地电模型下的数值成像,并采用多偏移距模式采集电磁波道集.分析了电磁波的波场快照图和波形剖面图,总结了电磁波在溶洞地质体中的传播规律,为实际工程勘察工作提供可靠依据.数值试验结果表明,FDTD(2,4)能高精度模拟电磁波在溶洞复杂介质中的数值成像和多偏移距采集模式具有高效性和灵活性.     

A Foreign Exchange Allocation Algorithm for the Acquisition of Key Spare Parts and Supplies in a Developing Country

Most developing countries are severely constrained by the size of their foreign exchange reserve necessary for the purchase on the international market of certain key items to be employed in their industries, including the export sectors that are responsible for generating the foreign exchange in the first place. The scarcity of this foreign exchange creates enormous problems for these countries. To cope with this dilemma, certain countries resort to all kinds of gambles and approaches that may not be defensible. A rational basis for the allocation of this scarce resource is described in this article. It consists primarily of two components. The first part deals with an optimal strategy for the identification of key items through a criticality assignment routine. The second relates to the algorithm for allocating foreign exchange to a pool of critical items to maximize the returns from such an allocation. The case study is Guyana, a developing country in South America.     

Empirical Modeling of a Hydraulic Actuator in a Vehicle Control System

The pressure information of a hydraulic actuator plays a key role in modern vehicle control and fault diagnosis. The difficulty in measuring pressure directly naturally motivates such an indirect approach as an observer whose accuracy depends heavily upon the availability of a high fidelity model of a hydraulic actuator. Notwithstanding its success in understanding the dynamics of the first principle model of a hydraulic actuator, it is not suited to controller/observer design due to its complexity. This paper presents an alternative to the first principle modeling methodology: an empirical approach to hydraulic actuator modeling. Linear and nonlinear system identification techniques are applied to obtain low-order models of a hydraulic actuator. Experimental results show how the empirical models reproduce the key features of a hydraulic actuator with sufficient accuracy.     

Loss Coefficients in Laminar Flows: Essential for the Design of Micro Flow Systems

The concept of head loss coefficients K for the determination of losses in conduit components is discussed in detail. While so far it has mainly been applied to fully turbulent flows it is extended here to also cover the laminar flow regime which is relevant for micro systems due to the low Reynolds numbers of these flows. Specific numbers of K can be determined by integration of the entropy generation field (second law analysis) obtained from a numerical simulation. It will be shown that a definition of K based on entropy generation is superior to a widely used definition that refers to a pressure drop caused by the conduit component. With the second law analysis details of the physics become available. For example it can be shown that often the main part of the entropy generation occurs downstream of the component. This aspect becomes important when several conduit components are combined in close proximity, like two 90 degree bends that are close to each other. Often in such situations the combination as a whole has to be looked upon as one new complex component. The general approach is discussed and illustrated for various conduit components and combinations of them. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Field validation of the geohydrology simulation model,FEWA

A finite element model of water flow through aquifers (FEWA) has been validated using field data from the Love Canal area, New York and from the Conesville area, Ohio, USA,The computed data for both cases investigated compare well with the field data, indicating that FEWA provides accurate results.     

Finite difference simulation of elastic wave propagation through 3D heterogeneous multiscale media based on locally refined grids

To simulate the interaction of seismic waves with microheterogeneities (like cavernous/fractured reservoirs), a finite difference technique based on grids locally refined in time and space is used. These grids are used because the scales of heterogeneities in the reference medium and in the reservoir are different. Parallel computations based on domain decomposition of the target area into elementary subdomains in both the reference medium (a coarse grid) and the reservoir (a fine grid) are performed. Each subdomain is assigned to a specific processor unit, which forms two groups: one for the reference medium, and the other for the reservoir. The data exchange between the groups within a processor unit is performed by non-blocking iSend/iReceive MPI commands. The data exchange between the two groups is performed simultaneously with coupling the coarse and a fine grids, and is controlled by a specially chosen processor unit. The results of a numerical simulation for a realistic model of fracture corridors are presented and discussed.     

人民币汇率对我国进出口的影响研究

自2005年7月人民币汇率制度改革至今,人民币对美元汇率不断升值.人民币的汇率升值作为一种对国内及国际经济的调节方式,对各行业经济发展的影响应该都是巨大的,尤其是对进出口的影响更是首当其中.基于2005年1月—2008年3月进出口、人民币对美元、欧元汇率等各项指标数据和VAR模型,得到了人民币汇率与进出口关系的向量误差修正模型,很好地解释了汇率变化对我国进出口行业的影响.     

SWAMP: A two‐dimensional hydrodynamic and quality modeling platform for shallow waters

Water quality two‐dimensional models are often partitioned into separate modules with separate hydraulic and biological units. In most cases this approach results in poor flexibility whenever the biological dynamics has to be adapted to a specific situation. Conversely, an integrated approach is pursued in this article, producing a two‐dimensional hydraulic‐water quality model, named Shallow Water Analysis and Modeling Program (SWAMP) designed for shallow water bodies. The major objective of the work is to create a comprehensive two‐dimensional water quality assessment tool, based on an open framework and combining easy programming of additional procedures with a user‐friendly interface. The model is based on the numerical solution of the partial differential equations describing advection‐diffusion and biological processes on a two‐dimensional rectangular finite elements mesh. The hydraulics and advection‐diffusion modules model were validated both with experimental tracer data collected at a constructed wetland site and a comparison with a commercial hydrodynamic software, showing good agreement in both cases. Moreover, the model was tested in critical conditions for mass conservation, such as time‐varying wet boundary, showing a considerable numerical robustness. In the last part of the article water quality simulations are presented, though validation data are not yet available. Nevertheless, the observed model response demonstrates general consistency with expected results and the advantages of integrating the hydraulic and quality modules. The interactive graphical user interface (GUI) is also shown to represent a simple and effective connective tool to the integrated package. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 663–687, 2002; DOI 10.1002/num.10014     

需求和汇率风险下的全球供应链汇率风险对冲策略

在下游零售商同时面临市场需求风险和汇率风险的背景下,研究了汇率风险对冲(外汇期货对冲)策略在全球供应链运作及风险管理中的作用。在无/有对冲策略两种情形下分别构建了上游制造商和下游零售商的动态博弈模型,并求解了均衡结果。两种情形下的均衡结果显示,汇率风险对冲策略可以提高供应链系统订货量、增加零售商收益的期望值和确定性等价量、增加供应链系统的总收益。进一步讨论了有对冲策略的情形下,两类外生风险对供应链均衡决策变量和盈利性的影响方式。结果表明,汇率风险对冲策略对汇率风险起到了有效的隔离作用,避免了供应链下游的汇率风险向上游企业传递,并能实现供应链收益与风险的权衡。