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.     

多特征流形鉴别嵌入的高分辨率遥感影像分类

针对高分辨遥感影像同谱异物、同物异谱导致单一特征分类结果精度较差的问题,本文提出了多特征流形鉴别嵌入的高分辨率遥感影像分类方法.该方法首先提取高分辨率影像数据的光谱特征与LBP纹理特征;然后通过样本数据的联合光谱、纹理特征的空间距离及对应的类别信息,构建影像对象的类间图与类内图,用于学习高分辨率影像上的鉴别流形结构,保...     

Initial stress formulae of high-order NMM and DDA for large deformation analysis

With high-order numerical manifold method (NMM) or high-order discontinuous deformation analysis method (DDA), computational accuracy of structure deformation can be improved greatly. However, poor accuracy is obtained and even computation is not convergent while treating large deformation problems, due to inaccurate or incorrect high-order initial stress formulae. Based on 2D triangular mathematical meshes and polynomial cover functions in high-order NMM, exact formulae for high-order initial stresses are deduced to depict configuration change of structures under large deformations. The formulae are expressed in polynomial forms so as to be used in simplex integrations. The approach is also extended to high-order DDA. Comparing with analytical solutions, accurate results for large deformation of a cantilever beam prove the validity of the proposed formulae.     

Tangential‐projection algorithm for manifold representation in unidentifiable model updating problems

The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. In an identifiable case, the posterior probability density function (PDF) of the uncertain model parameters for given measured data can be approximated by a weighted sum of Gaussian distributions centered at a number of discrete optimal values of the parameters at which some positive measure‐of‐fit function is minimized. The present paper focuses on the problem of model updating in the general unidentifiable case for which certain simplifying assumptions available for identifiable cases are not valid. In this case, the PDF is distributed in the neighbourhood of an extended and usually highly complex manifold of the parameter space that cannot be calculated explicitly. The computational difficulties associated with calculating the highly complex posterior PDF are discussed and a new adaptive algorithm, referred to as the tangential‐projection (TP) algorithm, allowing for an efficient approximate representation of the above manifold and the posterior PDF is presented. Using this approximation, expressions for calculating the uncertain predictive response are established. A numerical example involving noisy data is presented to demonstrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Motion Around The Triangular Equilibrium Points Of The Restricted Three-Body Problem Under Angular Velocity Variation

We study numerically the asymmetric periodic orbits which emanate from the triangular equilibrium points of the restricted three-body problem under the assumption that the angular velocity ω varies and for the Sun–Jupiter mass distribution. The symmetric periodic orbits emanating from the collinear Lagrangian point L ₃, which are related to them, are also examined. The analytic determination of the initial conditions of the long- and short-period Trojan families around the equilibrium points, is given. The corresponding families were examined, for a combination of the mass ratio and the angular velocity (case of equal eigenfrequencies), and also for the critical value ω = 2

Spatial hashing based contact detection for numerical manifold method

A spatial hashing method was introduced to accelerate the contact detection process in the numerical manifold method. All objects (blocks) in the work space are hashed to a one dimensional hash table based on a spatial grid, then only blocks within the same place in the hash table need to do contact detection. The proposed method has a time complexity of O(n). Experiments show that the spatial hashing contact detection has a significant improvement in performance.     

Evaluation of Reinforced Concrete Design for an Underground Outlet Manifold in Shanxi Yellow River Diversion Project

Summary In order to verify the design feasibility of the reinforced concrete lining of the outlet manifold in Shanxi Yellow River Diversion Project (YRDP), field investigations on rock mass deformability, in situ stress and hydraulic jacking measurements have been carried out. Based on the results obtained, 3-D FEM numerical analyses have been performed to calculate the stress distribution in a reinforced concrete lining under internal and external water pressure. Furthermore, the initial designed shape and steel ratio of concrete have been modified to satisfy the requirements for the limit crack width design criteria in China and decrease the tensile stress level in concrete. The new steel ratio of reinforced concrete has been calculated on the basis of the numerical results considering the modified shape of the outlet manifold. Both the owner and designer of YRDP have adopted the steel ratio of concrete in the working design and construction of the outlet manifold.     

A Class of higher dimensional spherically symmetric cosmological model in Lyra geometry

Exact analytical solutions are obtained for a higher dimensional spherically symmetric inhomogeneous metric in presence of a mass-less scalar field with a flat potential within the framework of Lyra geometry. Assuming a homogeneous scalar field, we have shown that the metric can be reduced to a generalized FRW type.     

Lagrangian singularities of steady two-dimensional flow

The Lagrangian complex-space singularities of the steady Eulerian flow with stream function sin x ₁ cos x ₂ are studied by numerical and analytical methods. The Lagrangian singular manifold is analytic. Its minimum distance from the real domain decreases logarithmically at short times and exponentially at large times.     

三维多值走时地震波场重建及格林函数计算

针对三维复杂介质地震波传播数值计算中出现的多值走时情况,阐述了地震波场重建及格林函数计算中的困难,提出一种在相空间拉格朗日流形上的波场重建及格林函数计算方法．本文算法应用于三维叠前深度偏移处理流程时,可高效地获得均匀网格点上地震波多值走时及振幅的数值计算结果．文中还阐明两类数值计算过程判据,以在多值走时区域及计算的全区域中,控制射线追踪过程中的射线密度及格林函数计算精度．算例验证了本文方法的有效性．