A monotone nonlinear finite volume method for diffusion equations and multiphase flows

We present a new nonlinear monotone finite volume method for diffusion equation and its application to two-phase flow model. We consider full anisotropic discontinuous diffusion or permeability tensors on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which provides the conventional seven-point stencil for the discrete diffusion operator on cubic meshes. We show that the quality of the discrete flux in a reservoir simulator has great effect on the front behavior and the water breakthrough time. We compare two two-point flux approximations (TPFA), the proposed nonlinear TPFA and the conventional linear TPFA, and multipoint flux approximation (MPFA). The new nonlinear scheme has a number of important advantages over the traditional linear discretizations. Compared to the linear TPFA, the nonlinear TPFA demonstrates low sensitivity to grid distortions and provides appropriate approximation in case of full anisotropic permeability tensor. For nonorthogonal grids or full anisotropic permeability tensors, the conventional linear TPFA provides no approximation, while the nonlinear flux is still first-order accurate. The computational work for the new method is higher than the one for the conventional TPFA, yet it is rather competitive. Compared to MPFA, the new scheme provides sparser algebraic systems and thus is less computational expensive. Moreover, it is monotone which means that the discrete solution preserves the nonnegativity of the differential solution.     

A comparison between finite element and finite difference explicit formulations for triangular and quadrilateral plane-strain elements

For non-linear dynamic problems, it has been recognized that an explicit time-integration method of approach is a very efficient way of solving the dynamic equations of motion. The numerical formulation and computation for such problems fall into the two general categories of finite elements and finite differences. Over the years, there have been many arguments between schools which adopt the finite element approach and those which adopt the finite difference approach. At one extreme, arguments areconcerned with the superiority of each approach and at the other end of the spectrum the arguments are about which approach is a subset of the other. The most common of these arguments are concerned with efficiency and accuracy. This publication addresses the accuracy issue with specific reference to explicit calculations in which the analysis domain is discretized into triangular or quadrilateral plane-strain elements. It concludes that if the same basic assumptions are made in the two approaches, they, will give identical answers for problems in this category.     

A numerical method for the solution of the nonlinear turbulent one-dimensional free surface flow equations

Free surface flow of an incompressible fluid over a shallow plane/undulating horizontal bed is characteristically turbulent due to disturbances generated by the bed resistance and other causes. The governing equations of such flows in one dimension, for finite amplitude of surface elevation over the bed, are the Continuity Equation and a highly nonlinear Momentum Equation of order three. The method developed in this paper introduces the “discharge” variable q = η U, where η = elevation of the free surface above the bed level, and U = average stream-wise forward velocity. By this substitution, the continuity equation becomes a linear first-order PDE and the momentum equation is transformed after introduction of a small approximation in the fifth term. Next, it is shown by an invertibility argument that q can be a function of η: q = F(η), rendering the momentum equation as a first order, second degree ODE for F(η), that can be be integrated by the Runge-Kutta method. The continuity equation then takes the form of a first order evolutionary PDE that can be integrated by a Lax-Wendroff type of scheme for the temporal evolution of the surface elevation η. The method is implemented for two particular cases: when the initial elevation is triangular with vertical angle of 120 ^° and when it has a sinusoidal form. The computations exhibit the physically interesting feature that the frontal portion of the propagating wave undergoes a sharp jump followed by tumbling over as a breaker. Compared to other discretization methods, the application of the Runge-Kutta and an extended version of the Lax-Wendroff scheme is much easier.     

A computer program for the determination of finite strain using fry method

Fry method enables rapid estimate of finite strain from deformed aggregates such as clastic grains, fossil colonies, oolitic or pisolitic aggregates, prophyroblastic minerals or phenocrysts. It has an advantage over the other methods of finite strain analysis in its very quality of enabling rapid estimation with a reasonable degree of accuracy. Details of the software to prepare a plot using Fry method are outlined. This program has an advantage over other computer based programs on the world wide web in its aesthetic getup, small size, user friendliness and a help file.     

无结构网格上平面二维水沙模拟的有限体积法

基于无结构网格有限体积法的算法框架,通过引入跨单元界面法向水沙数值通量的逆风分解,将悬沙与床沙交换以及分组挟沙力计算模式自然地嵌入二维水沙运动方程组的数值格式中,形成高精度、守恒性好的二维水沙有限体积算法。最后,利用该算法对谭江樟州河段的水沙输运和河床变形进行了数值模拟。结果表明,该算法能够较好地模拟复杂条件下河道水沙输运的往复特征和河床变形的动态过程,其精度满足河道工程后效分析的要求。     

A coupled time integration algorithm for discontinuous deformation analysis using the numerical manifold method

To improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial-domain coupled explicit-implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration-based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses.     

A design method for plastic tube cast-in-place concrete pile considering cavity contraction and its validation

Bearing capacity calculation method and field static load test (SLT) program were carried out simultaneously to study the bearing characteristics of individual Plastic Tube Cast-in-Place Concrete Pile (TC pile), which are increasingly being employed for support of embankments in southeast China. The bearing capacity calculation method considering pile setup (i.e., setup calculation method) was built up according to the cylindrical cavity contraction and horizontal consolidation theories. A series of SLTs on different dates were applied to study the bearing behavior of TC pile and to verify the validity of the established setup calculation method. During TC piles installation, there is about 45% contraction in cylindrical volume due to the extraction of steel casing. Both theoretical and experimental results show that the calculated outcomes considering cylindrical cavity contraction agree well with measured ones. The difference value between them is not more than 12%. On the other hand, if the cylindrical cavity contraction is ignored, the calculated bearing capacities of TC piles are overestimated by 160–300%. The setup of TC pile is mainly due to the increment of pile shaft resistance with time elapsed. Cylindrical cavity contraction accompanied by TC pile installation causes much loss of pile shaft resistance.     

黄河下游非恒定输沙数学模型——Ⅰ模型方程与数值方法

构建起具有通用性的黄河下游一维非恒定输沙数学模型.该模型建立了新的泥沙连续性方程与河床变形方程,克服了以往数学模型计算中取饱和恢复系数小于1等缺陷,引入了符合黄河下游河道水沙特点的水流挟沙力和河床糙率计算等公式,给出了悬移质含沙量以及悬移质泥沙平均粒径沿横向分布的计算方法,以及阐明了河槽在冲淤过程中河宽变化规律的模拟技术.运用Preissmann四点差分格式离散水流方程,并与泥沙连续性方程进行非耦合求解.     

黄河下游非恒定输沙数学模型——Ⅰ模型方程与数值方法

构建起具有通用性的黄河下游一维非恒定输沙数学模型.该模型建立了新的泥沙连续性方程与河床变形方程,克服了以往数学模型计算中取饱和恢复系数小于1等缺陷,引入了符合黄河下游河道水沙特点的水流挟沙力和河床糙率计算等公式,给出了悬移质含沙量以及悬移质泥沙平均粒径沿横向分布的计算方法,以及阐明了河槽在冲淤过程中河宽变化规律的模拟技术.运用Preissmann四点差分格式离散水流方程,并与泥沙连续性方程进行非耦合求解.     

A coupling scheme for boundary and finite elements using a joint element

A coupling scheme for boundary and finite elements using a joint element is proposed. The scheme is based on the finite element discretization (i.e. the equivalent FE procedure). Footing problems founded on multiple layers are solved. Furthermore, the scheme is extended to a non-linear analysis.     

网络并行电法与传统电法超前探测效果对比

网络并行电法是以分布式并行智能电极电位差信号采集方法为技术核心支撑的直流电法,其数据采集模拟地震勘探方式进行,与常规电法每次供电只能采得一个测点数据不同,并行电法每次供电可同时获得多个测点数据,是一种全电场观测技术。运用两种方法对龙岩市新罗区大弯煤矿和武平荧石矿进行超前探测试验对比研究,并经实际巷道掘进揭露验证,表明网络并行电法技术较传统电法技术效果更好,效率更高。     

相邻基坑有限宽度土条主动土压力的计算

同步开挖的相邻基坑间有限宽度土条不同于以往的邻近既有建筑基坑的有限土条,其破坏方向未知,破坏形式多样,土条两侧的主动土压力计算不能沿用以往的研究成果来扩展应用。借鉴筒仓受力原理应用于相邻基坑间的土条分析计算,通过力学平衡分析和微分方程求解,得出基坑开挖中两侧均为支护结构的有限宽度土条（砂土和黏性土）的主动土压力计算公式,该公式输入参数少、假设条件少,使用方便。对比朗肯主动土压力计算公式和有限元数值模拟计算结果,该计算公式与有限元模拟计算结果基本一致,在相同深度处计算的土压力远小于朗肯土压力。     

A two level scaling-up method for multiphase flow in porous media; numerical validation and comparison with other methods

We present a robust and accurate strategy for upscaling two-phase flow in heterogeneous porous media composed of different rock-types. The method is tested by means of numerical simulations and compared with other upscaling methods.     

A fast method for the solution of a system of simultaneous linear equations—A method adapted to a particular problem

Mathematical Geosciences - In mineral deposit evaluation, the estimation of block values can involve the solution of as many as 100,000 systems of linear equations. To minimize computing costs it...     

成矿单元划分原则和方法探讨

本文强调,区域成矿图的编制原则和方法虽然应当以大地构造为基础,但却更应考虑成矿作用本身。成矿作用本身是确定成矿单元及其边界的首要因素。笔者在文中仍采用了成矿省这一概念。但与前人的用法不同,在这里,成矿省不仅具有空间概念,更为重要的是它具有时间属性。本文所说的成矿省是指在一定大地构造基础上,在相同或相似的地质背景中,在相同或相近的成矿时代,经相同或相关的成矿作用所形成的一种或彼此相关的几种矿床的分布范围。在此基础上划分成矿区(带)、成矿潜力区和成矿远景区。成矿区(带)是指根据所存在的矿床分布情况和成矿有利地质条件划分出的成矿单元。成矿潜力区是根据成矿有利地质条件划分出的成矿单元;潜力区内有时会存在有关矿床的矿化显示。成矿远景区是根据成矿有利地质条件推测(预测)出的成矿单元。根据这一思路,笔者提出了成矿单元的划分步骤以及在大地构造基础上划分成矿单元的原则框架,将克拉通地区的成矿单元按克拉通基底发展阶段、克拉通盖层发展阶段和后克拉通发展阶段划分成矿省;将造山带地区的成矿单元按造山带发展早期阶段、造山带发展晚期阶段和后造山带发展阶段划分成矿省;与基性-超基性岩带有关的矿床按其发育的断裂带、裂谷带和蛇绿岩带划分成矿单元。在克拉通和造山带晚期特别是后期发育的成矿单元,其界线可能与大地构造界线不尽一致甚至可能穿越构造界线。笔者结合中国情况对成矿单元进行了初步划分,例如华北克拉通东端的胶—辽菱镁矿-滑石-石墨成矿省、华北克拉通北缘的燕—辽铁-金成矿省、西秦岭华力西造山带的西秦岭铅锌成矿省和大兴安岭华力西造山带的大兴安岭多金属-铁成矿省以及这些成矿省中的成矿潜力区和远景区等等。这样的划分,实际上已经预示了找矿范围和找矿方向。     

Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method

In the numerical modeling of fluid flow in heterogeneous geological media, large material contrasts associated with complexly intersected material interfaces are challenging, not only related to mesh discretization but also for the accurate realization of the corresponding boundary constraints. To address these challenges, we developed a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method (NMM) and the Lagrange multiplier method (LMM) for modeling boundary constraints. The advantages of NMM include meshing efficiency with fixed mathematical grids (covers), the convenience of increasing the approximation precision, and the high integration precision provided by simplex integration. In this discontinuous approach, the elements intersected by material interfaces are divided into different elements and linked together using the LMM. We derive and compare different forms of LMMs and arrive at a new LMM that is efficient in terms of not requiring additional Lagrange multiplier topology, yet stringently derived by physical principles, and accurate in numerical performance. To demonstrate the accuracy and efficiency of the NMM with the developed LMM for boundary constraints, we simulate a number of verification and demonstration examples, involving a Dirichlet boundary condition and dense and intersected material interfaces. Last, we applied the developed model for modeling fluid flow in heterogeneous media with several material zones containing a fault and an opening. We show that the developed discontinuous approach is very suitable for modeling fluid flow in strongly heterogeneous media with good accuracy for large material contrasts, complex Dirichlet boundary conditions, or complexly intersected material interfaces. Copyright © 2015 John Wiley & Sons, Ltd.     

A quasi-classical method for deriving the equations of radiative transfer in a magnetic field

A new derivation of the matrix equations of radiative transfer in a magnetic field is presented, which is based on the classical approach of M. Born and V.E. Stepanov. Convenient vector relations making it possible to formulate the radiative-transfer equations in an arbitrary coordinate system and choose a convenient system of Stokes parameters are presented. The cases of the solar atmosphere and a stellar atmosphere with a dipolar magnetic field are presented as examples. The use of the radiative-transfer equations written in terms of two main oscillation components (the method of V.E. Stepanov) can lead to crude errors when the complex nature of the absorption coefficients is taken into account.     

A simple method for calculating displacements and stresses around tunnel openings an application for the microcomputer

SummaryA Simple Method for Calculating Displacements and Stresses Around Tunnel Openings — An Application for the Microcomputer The paper describes a program, written for an Apple-II/Plus Microcomputer, and designed to calculate the perimetral elastic deformations and tangential stresses around underground openings of non-circular section. The mathematical basis used in this program first appeared in a paper by Dr. E. Wisser, published in Rock Mechanics. The Appendix gives the list of the program and all instructions which a user, familiar with computers, may require.With 5 Figures     

A new method of estimating the ratio between in situ rock stresses and tectonics based on empirical and probabilistic analyses

This paper describes a new procedure for assessing the ratio between in situ stresses in rock masses by means of K (K = σ_H / σ_v, being σ_H and σ_v principal stress) and tectonics for purposes of engineering geology and rock mechanics. The method combines the use of the logic decision tree and the empirical relationship between the Tectonic Stress Index, TSI, and a series of K in situ values obtained from an extensive database. The decision tree considers geological and geophysical factors affecting stress magnitudes both on the regional and local scale. The TSI index is defined by geological and geomechanical parameters. The method proposed provides an assessment of the magnitude of horizontal stresses of tectonic origin. Results for several regions of Europe are presented and the possible applications of the procedure are discussed.     

A new combined framework for sustainable development using the DPSIR approach and numerical modeling

Relying on the conceptual DPSIR framework and MODFLOW analysis,this study used a mixed approach to produce groundwater resource management solutions for the Najafabad area in central Iran.According to DPSIR results,agricultural activities put the highest pressure on groundwater resources in this region.The results showed the effectiveness of reducing water withdrawal over 30 years in maintaining the aquifer in a state of equilibrium.The best scenario consisted of cutting down extraction by 10% over the said period.Output maps of the water table rise at the Najafabad aquifer clearly showed that the groundwater management scenario involving a 10% reduction of water withdrawal was the most effective solution,as it would raise the water level by 6.7 m.Regarding other scenarios,reducing cultivated area by 20% was found to raise the water table by 5.03 m on average,while cutting down water withdrawal by 5% increased the water table by 3.6 m,and a 10% reduction of the cultivated area resulted in a 1.85 m rise.The combined model proposed here can be used for similar aquifers and can aid decision-makers and managers.