Operator splitting methods for degenerate convection–diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation

We present an accurate numerical method for a large class of scalar, strongly degenerate convection–diffusion equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation–consolidation processes. The method is based on splitting the convective and the diffusive terms. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion part is solved by an implicit–explicit finite difference scheme. In addition, one version of the implemented operator splitting method has a mechanism built in for detecting and correcting unphysical entropy loss, which may occur when the time step is large. This mechanism helps us gain a large time step ability for practical computations. A detailed convergence analysis of the operator splitting method was given in Part I. Here we present numerical experiments with the method for examples modelling secondary oil recovery and sedimentation–consolidation processes. We demonstrate that the splitting method resolves sharp gradients accurately, may use large time steps, has first order convergence, exhibits small grid orientation effects, has small mass balance errors, and is rather efficient.     

Discrete Element Modeling of Stress and Strain Evolution Within and Outside a Depleting Reservoir

Stress changes within and around a depleting petroleum reservoir can lead to reservoir compaction and surface subsidence, affect drilling and productivity of oil wells, and influence seismic waves used for monitoring of reservoir performance. Currently modeling efforts are split into more or less coupled geomechanical (normally linearly elastic), fluid flow, and geophysical simulations. There is evidence (from e.g. induced seismicity) that faults may be triggered or generated as a result of reservoir depletion. The numerical technique that most adequately incorporates fracture formation is the DEM (Discrete Element Method). This paper demonstrates the feasibility of the DEM (here PFC; Particle Flow Code) to handle this problem. Using an element size of 20 m, 2-D and 3-D simulations have been performed of stress and strain evolution within and around a depleting reservoir. Within limits of elasticity, the simulations largely reproduce analytical predictions; the accuracy is however limited by the element size. When the elastic limit is exceeded, faulting is predicted, particularly near the edge of the reservoir. Simulations have also been performed to study the activation of a pre-existing fault near a depleting reservoir.     

The Displacement and Strain Field of Three-dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains ε_xx (r, t), ε_yy (r, t) and ε_zz (r, t) and the bulk strain θ (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (α, β, γ) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.     

点特征提取算法探讨

影像特征提取是影像匹配和三维信息提取的基础,是影像分析与单像处理技术领域中最重要的任务之一。有效的特征提取算法是影像分析与处理的关键。从点特征定义出发,叙述了两种常用的点特征提取算子---Moravec算子和Forstner算子的原理,利用Moravec算子和Forstner算子可以实现影像点特征的提取,并从提取点特征的准确度、提取速度对两种算子进行比较,最后得出了有益的结论。     

数学形态学在二值数字图像断续线形目标恢复上的应用

特征提取中,由于地物特征的差异及其它因素的影响,提取的目标大多是非连续的,这将导致提取的目标与实际情况不符合,若不进行恢复,势必影响对目标性质的认识和应用。本文基于数学形态学方法,首先对二值图像中非连续的线性目标进行了分析和处理,然后对结构元素的选取和分解进行了阐述。最后的实验结果表明,该方法效果较好。     

Numerical studies of shear banding in interface shear tests using a new strain calculation method

Strain localization is closely associated with the stress–strain behaviour of an interphase system subject to quasi‐static direct interface shear, especially after peak stress state is reached. This behaviour is important because it is closely related to deformations experienced by geotechnical composite structures. This paper presents a study using two‐dimensional discrete element method (DEM) simulations on the strain localization of an idealized interphase system composed of densely packed spherical particles in contact with rough manufactured surfaces. The manufactured surface is made up of regular or irregular triangular asperities with varying slopes. A new simple method of strain calculation is used in this study to generate strain field inside a simulated direct interface shear box. This method accounts for particle rotation and captures strain localization features at high resolution. Results show that strain localization begins with the onset of non‐linear stress–strain behaviour. A distinct but discontinuous shear band emerges above the rough surface just before the peak stress state, which becomes more expansive and coherent with post‐peak strain softening. It is found that the shear bands developed by surfaces with smaller roughness are much thinner than those developed by surfaces with greater roughness. The maximum thickness of the intense shear zone is observed to be about 8–10 median particle diameters. The shear band orientations, which are mainly dominated by the rough boundary surface, are parallel with the zero extension direction, which are horizontally oriented. Published in 2007 by John Wiley & Sons, Ltd.     

离散KL变换在航磁轴向异常计算机检测中的应用

目前航磁异常的计算机检测手段单一,现有检测方法停留在定性研究的水平上,无法适应实际需要。为了克服这些局限性,将航磁异常计算机检测结果从定性水平提升到定量水平,这里提出了将图像处理中的离散KL变换方法应用于航磁轴向异常检测的新思想。经实地实例检验,效果良好,这一思想对研究航磁异常计算机检测有一定的借鉴意义。     

Marr方法在多波段遥感影像边缘信息分析中的应用

简要介绍了Marr理论的基本框架，并详细介绍了Marr-Hildreth边缘检测理论的基本原理，同时给出了LOG模板算子实例。在此基础上，提出这一理论用于多波段影像边缘分析的几种不同的方法，指出了本文所采取方法的原理和算法流程。试验结果的分析对比说明，多波段影像分析的效果优于单波段。     

Discrete‐time variable structure control of seismically excited building structures

Generally, the active structural control system belongs to the discrete‐time control system, and the sampling period is one of the most important factors that would directly affect the performance of the control system. In this paper, active control approaches by using the discrete‐time variable structure control theory are studied for reducing the dynamic responses of seismically excited building structures. Based on the discrete reaching law method, a feedback controller which includes the sampling period is presented. The controller is extended by introducing the saturated control method to avoid the adverse effect when the actuators are saturated due to unexpected extreme earthquakes. The simulation results are obtained for a single‐degree‐of‐freedom (SDOF) system and a MDOF shear building equipped with active brace system (ABS) under seismic excitations. It is found that the discrete variable structure control approach and its saturated control method presented in this paper are quite effective. Copyright © 2001 John Wiley & Sons, Ltd.     

小波多尺度影像边缘聚焦算法

讨论了基于光滑函数的二维小波极大模边缘算子和小波过零点边缘算子及其特性。提出了多尺度二进小波变换过零点边缘聚焦算法。通过对不同尺度下小波变换的遥感影像进行复合、边缘提取和聚焦后结果进行比较，可以发现该算法适应影像空间尺度不确定性目标边缘提取。既可保证大尺度下的轮廓信息不失真，又能在边缘定位上保持很高的精度。