An efficient parallel mixed method for flow simulations in heterogeneous geological media

The permeability of a 3D geological fracture network is determined by triangulating the fractures and solving the 2D Darcy's equation in each fracture. Here, the numerical modelling aims to simulate a great number of networks made up of a great number of fractures i.e. from 10³ to 10⁶ fractures. Parallel computing allows us to solve very large linear systems improving the realism of simulations. Several algorithms to simulating fluid flow are proposed for the cases of significant matrix permeability. In the case of a weak permeability matrix, the flow is focused in the fractures having a strong permeability and fluids percolate through networks of interconnected fractures. In this paper, we present a complete parallel algorithm for solving flow equations in fracture networks. We consider an imprevious matrix. The different parts of the algorithm are detailed. Numerical examples using the mixed finite element (MFE) method for various fracture networks illustrate the efficiency and robustness of the proposed algorithm. To the best of our knowledge, results for parellel simulation of fluid flow in discrete-fractured media with impervious matrix using the MFE method are the first to appear in the literature.     

Particles’ transport in a single fracture under variable flow regimes

A mathematical model to account for non-laminar terms, during simulated transports in fractured rocks has been developed. The relevant conceptual model consists of a two dimensional grid block equivalent to a variable fracture plane. The block aperture variability is expressed by means of stochastic procedures, based upon some characteristics of fractured media. One of them, e.g. the equivalent hydraulic aperture, may be estimated by means of the results of field tests. The solution of Navier–Stokes and Darcy–Weisbach's equation for steady state flow between two parallel plates with constant aperture allows the systems of equations under respetively, laminar and non-laminar conditions, to be wirtten. The flow model is a standard finite-difference method with a modified version of Darcy's equation to account for non-laminar terms that are important at high water velocity. To simulate solute transports, the particle tracking technique was applied.     

Stratified smooth two-phase flow using the immersed interface method

The immersed interface method is used to derive a numerical method for solving fully developed, stratified smooth two-phase flow in pipes. This sharp interface technique makes the representation of the interface independent of the grid structure, and it allows for using an arbitrary shaped interface. The two-dimensional steady-state axial momentum equation is discretized and solved using a finite difference scheme on a composite, overlapping grid with local grid refinement near the interface and near the pipe wall. A low Reynolds number k-ε turbulence model is adopted to account for the effect of turbulence. A level set function is used to represent the interface. Numerical results are presented for laminar and turbulent flows. The numerical method compares well with analytical solution for laminar flow, and it shows acceptable agreement with experimental data for turbulent flow. A few examples are given to demonstrate the capability of the method to solve flow problems with a complex shaped interface.     

The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids

An abstract framework ofauxiliary space method is proposed and, as an application, an optimal multigrid technique is developed for general unstructured grids. The auxiliary space method is a (nonnested) two level preconditioning technique based on a simple relaxation scheme (smoother) and an auxiliary space (that may be roughly understood as a nonnested coarser space). An optimal multigrid preconditioner is then obtained for a discretized partial differential operator defined on an unstructured grid by using an auxiliary space defined on a more structured grid in which a furthernested multigrid method can be naturally applied. This new technique makes it possible to apply multigrid methods to general unstructured grids without too much more programming effort than traditional solution methods. Some simple examples are also given to illustrate the abstract theory and for instance the Morley finite element space is used as an auxiliary space to construct a preconditioner for Argyris element for biharmonic equations. Some numerical results are also given to demonstrate the efficiency of using structured grid for auxiliary space to precondition unstructured grids.     

基于裂隙方向的岩石节理裂隙缝合

在许多岩体工程应用中,识别岩体裂隙非常重要。运用图像处理方法识别岩体裂隙并实现自动缝合在岩体裂隙识别中非常困难并且至关重要。在实验室和工作中,新近开发的岩体节理裂隙缝合算法对裂隙缝合非常有效。     

一种基于压缩感知的离格阵列测向方法

基于稀疏表示的阵列测向技术中的一系列高精度鲁棒性方法都基于网格假设,即假设入射信号来向无误差地落在网格上,这一假设与现实中信号来向落在连续角度域内相违背,所造成的网格偏差效应会带来模型失配,从而导致估计性能的恶化。针对这一问题,本文提出了一种基于泰勒展开的离格类信号模型,该模型允许信号来向偏离网格,从而消除了网格误差效应,减小了估计误差。同时采用一种交替迭代优化的方法对模型进行求解,并利用奇异值分解等方法降低计算量。该方法能够有效减小网格误差,提高估计精度。仿真结果验证了所提方法的有效性。     

A novel synchronization scheme for grid-connected converters by using adaptive linear optimal filter based PLL (ALOF–PLL)

This paper proposes a novel grid synchronization scheme using a new phase-locked loop (PLL) scheme based on the adaptive linear optimal filtering (ALOF) technique. The problem formulation of the proposed ALOF is based on decomposing grid voltage signal into inner product of two vectors, namely, the vector of trigonometric functions and the vector of coefficients, corresponding to the input vector and the weight vector of the closed-loop adaptation algorithm by using least-mean-square (LMS) optimization algorithm. The coefficient of the fundamental component of the grid voltage is used as input signal for the PLL and the phase angles of the trigonometric functions are obtained from the output of the PLL recursively. The mathematical derivation of the weights updating law and the stability analysis of the ALOF–PLL are presented. Besides, the parameter selection for optimal performance is also discussed in terms of continuous domain (s-domain) analysis, discrete domain (z-domain) analysis and time domain simulations. The proposed ALOF–PLL shows the characteristic of band-pass filter at fundamental frequency and a notch filter at the harmonic frequencies. Finally, a detailed comparison with the existing single-phase and three-phase grid synchronization methods is also presented, and the proposed ALOF–PLL is found to have overwhelming advantages over the existing grid synchronization methods in terms of tracking accuracy, dynamic response and immunity to grid voltage disturbances, such as voltage sag/swell, phase-angle jump, harmonics, unbalance, random noises and frequency jump, etc. The validity and effectiveness of the ALOF–PLL is substantially confirmed by the extensive simulation results obtained from Matlab/Simulink.     

Incompletely Coupled Equations of Hydraulic Fracturing

We study a three-dimensional coupled problem of the creeping flows of a viscous fluid in a hydraulic (and magmatic) fracture and the strain and flow in the external poroelastic medium induced by them. The process is governed by injection fluid into a well. The flow in the fracture is described by the Stokes hydrodynamic equations in the approximation of the lubricating layer. The external problem is described by the equations of poroelasticity. An ordered sequence of interdependent geomechanical processes occurring under hydraulic (and magma) fracturing is established. In other words, the solution of the coupled problem of hydraulic fracturing is reduced to the sequential solution of three incompletely coupled problems representing the motion in the fracture, as well as the elastic and flow processes in the host rock. The proposed transformation is of practical importance for petroleum geophysics; it allows conducting a more profound in-depth study of the nonisothermal and physicochemical phenomena for occurring in the above-mentioned fractures; and it provides a better insight into the physics of the associated processes.     

One-time proxy signatures revisited

Proxy signatures are useful constructions in grid computing, mobile agents and many other emerging applications. In a recent work [Huaxiong Wang and Josef Pieprzyk: Efficient One-Time Proxy Signatures. Proc. ASIACRYPT'03, LNCS 2894, Springer 2003.], Wang and Pieprzyk proposed a one-time signature scheme which allows full delegation to a proxy with an added feature that allows tracing the authorship of the signature in case of a dispute. In this paper we present a simple alternative approach that eliminates public-key cryptography in key generation, offers certainty and simplicity in the dispute resolution and avoids swallow attacks. We also introduce the concept of 1-out-of-n threshold traceable one-time signatures as an efficiency improvement.     

Meshing of porous foam structures on the micro-scale

A semi-automatic block-structured grid generation technique for hexahedral meshing of porous open cell Kelvin foam structures for investigation of the pore scale fluid flow is presented. The performance of the algorithm is compared with a tetrahedral full automatic Delaunay meshing technique. In the first part of the paper the meshing strategies are explained. In the second part grid generation times, simulation times and the mesh quality are evaluated. For this Computational Fluid Dynamics (CFD) simulations for both a diffusion-dominated case (Re = 0.129) and a convection-dominated case (Re = 129) are carried out and analysed on four different cell resolutions of each mesh type. For the quality evaluation three different a posteriori error estimates are studied for the two mesh types on the different mesh sizes. The results are: the block-structured grid generation technique is about 10–20 times faster than the tetrahedral full automatic technique. While the mean field error estimates are comparable for both meshes, the maximum field error estimates for the block-structured meshes are only half of those for the tetrahedral meshes. Reaching simulation results of the same quality the hexahedral mesh needs about 20–40% less iterations with comparable mesh sizes. The time per iteration for the hexahedral meshes are up to 94% smaller than for the tetrahedral meshes. This makes the semi-automatic block-structured grid generation technique especially suitable for parameter studies and for the investigation of micro-scale flows in foam structures consisting of large quantities of Kelvin cells.     

On simultaneous straight-line grid embedding of a planar graph and its dual

Simultaneous representations of planar graphs and their duals normally require that the dual vertices to be placed inside their corresponding primal faces, and the edges of the dual graph to cross only their corresponding primal edges. Erten and Kobourov [C. Erten, S.G. Kobourov, Simultaneous embedding of a planar graph and its dual on the grid, Theory Computer Systems 38 (2005) 313-327] provided a linear time algorithm on simultaneous straight-line grid embedding of a 3-connected planar graph and its dual such that all the vertices are placed on grid points and each edge is drawn as one straight-line segment except for one which is drawn using two segments. Their drawing size is (2n−2)×(2n−2), where n is the total number of vertices in the graph and its dual. They raised an open question on whether there is a large class of planar graphs that allows this simultaneous straight-line grid embedding on a smaller grid. We answer this open question by giving a linear time simultaneous straight-line grid embedding algorithm for a 3-connected planar graph and its dual on a grid of size (n−1)×n.     

遗传算法的阶梯电价用电需求管理方案

用电需求管理是智能电网中的重要部分,能让消费者根据自己的用电量做出合适的决策,帮助供电者减少峰值负载,让负载的时空分布更为均衡,从而增加智能电网的可持续性,并减少运营成本和碳排放量。一种基于负载转移技术的用电需求管理方案可以满足对大量、多种设备的调节需求。用电需求管理的解决方案使用改进的遗传算法,并引入了一个新的算子,模拟测试的结果显示通过改进的算法获得的方案节省了可观的成本,并且在使用阶梯式电价的情况下,减少了智能电网的峰值负载。     

An elimination approach for fast parallel solution of the model fourth-order elliptic problem

A fast algorithm is developed for the parallel numerical solution of the first biharmonic boundary value problem on a rectangular region with N² interior grid points. The parallel computer considered is of SIMD type. The iterative procedure where one iteration consists in solving two transformed Poisson equations with relaxation is used. This approach allows one to apply the direct block-elimination method with parallel algorithm for linear recurrence relations efficiently to the evaluation of one iteration. For our algorithm the time per iteration does not exceed 9 log N time units, on N² processors. Thus, the technique presented brings a reduction in the arithmetic steps required for the solution of the problem considered.     

A top-k spatial join querying processing algorithm based on spark

Aiming at the problem of top-k spatial join query processing in cloud computing systems, a Spark-based top-k spatial join (STKSJ) query processing algorithm is proposed. In this algorithm, the whole data space is divided into grid cells of the same size by a grid partitioning method, and each spatial object in one data set is projected into a grid cell. The Minimum Bounding Rectangle (MBR) of all spatial objects in each grid cell is computed. The spatial objects overlapping with these MBRs in another spatial data set are replicated to the corresponding grid cells, thereby filtering out spatial objects for which there are no join results, thus reducing the cost of subsequent spatial join processing. An improved plane sweeping algorithm is also proposed that speeds up the scanning mode and applies threshold filtering, thus greatly reducing the communication and computation costs of intermediate join results in subsequent top-k aggregation operations. Experimental results on synthetic and real data sets show that the proposed algorithm has clear advantages, and better performance than existing top-k spatial join query processing algorithms.     

Direct solution of the equation for the Stokes stream function

Iterative procedures for solving the Stokes stream function equation can be quite time-consuming. This paper presents a direct procedure which can be used when the stream function vanishes on the periphery of a meridional-plane rectangle, one side of which is the axis of symmetry. The development allows for the possibility that the axial coordinate has been “stretched” in order to concentrate grid points in preselected bands. The resulting algorithm is, in fact, only marginally simpler if the coordinate is unstretched.Most steps of the development involve only classical methods of matrix algebra. The numerical technique is a matrix analog of the method of separation of variables for solving partial differential equations. One key step does employ a relatively modern technique — the QL algorithm for diagonalizing a symmetric tridiagonal matrix. Implementation of that algorithm has been comprehensively documented in the literature of the subject.     

The virtual crack extension method for nonlinear material behavior

The linear elastic, stiffness-derivative, finite element technique of Parks [ 1 ]is generalized to determine the ductile fracture parameter J from elastic-plastic finite element solutions. The method, based on energy comparison of two slightly different crack lengths, requires only one elastic-plastic finite element solution, and the altered crack configuration is obtained by changing nodal point positions. The technique is applied to finite element solutions for a deeply cracked, plane-strain bend specimen - a configuration for which J can be otherwise obtained - and the results are encouraging. The extension of the method to obtain arc-length-weighted J values in three-dimensional crack configurations is also proposed.     

Numerical analysis of hydraulically-driven fractures

A general method-of-lines numerical approach for modeling hydraulically-driven fractures is developed and tested. The methodology employs several novel features: a straining coordinate system that elongates as the fracture grows, an evolutionary equation to describe growth of the fracture length, direct treatment of the fluid/elastic-solid coupling, and a control volume equation which governs fluid motion near the tip and thus circumvents local degeneracy of the differential equations. Spatial discretization of the governing equations leads to a nonsparse system of implicit, coupled ordinary differential equations that is solved for time derivatives that are then integrated with a Runge-Kutta algorithm. The numerical solutions agree very well with known similarity solutions for laminar and for turbulent flow. New solutions for nonsimilar flows are also presented and these converge to proper limits as the fracture becomes very long. Acceptable accuracy, in all cases, is obtained using a very few numerical grid points and with modest execution times.     

Hand gesture recognition using a neural network shape fitting technique

A new method for hand gesture recognition that is based on a hand gesture fitting procedure via a new Self-Growing and Self-Organized Neural Gas (SGONG) network is proposed. Initially, the region of the hand is detected by applying a color segmentation technique based on a skin color filtering procedure in the YCbCr color space. Then, the SGONG network is applied on the hand area so as to approach its shape. Based on the output grid of neurons produced by the neural network, palm morphologic characteristics are extracted. These characteristics, in accordance with powerful finger features, allow the identification of the raised fingers. Finally, the hand gesture recognition is accomplished through a likelihood-based classification technique. The proposed system has been extensively tested with success.     

Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement

A numerical method for 2D LEFM crack propagation simulation is presented. This uses a Lepp–Delaunay based mesh refinement algorithm for triangular meshes which allows both the generation of the initial mesh and the local modification of the current mesh as the crack propagates. For any triangle t, Lepp(t) (Longest Edge Propagation Path of t) is a finite, ordered list of increasing longest edge neighbor triangles, that allows to find a pair of triangles over which mesh refinement operations are easily and locally performed. This is particularly useful for fracture mechanics analysis, where high gradients of element size are needed. The crack propagation is simulated by using a finite element model for each crack propagation step, then the mesh near the crack tip is modified to take into account the crack advance. Stress intensify factors are calculated using the displacement extrapolation technique while the crack propagation angle is calculated using the maximum circumferential stress method. Empirical testing shows that the behavior of the method is in complete agreement with experimental results reported in the literature. Good results are obtained in terms of accuracy and mesh element size across the geometry during the process.     

基于紫外光图像的岩石裂隙骨架抽取

利用数字图像技术对基于紫外光的岩石裂隙图像进行裂隙骨架抽取。首先对岩石裂隙图像进行噪声滤除、图像分割、空腔填充、短枝去除等图像处理操作,然后在分析了骨架特性和骨架抽取算法的基础上提出了基于结构元素的逐层细化算法。经实验得知,该算法可以高效地抽取较理想的岩石裂隙骨架,且算法稳定,行之有效。