Divergence of solutions to perturbation-based advection-dispersion moment equations     

Kenneth D. Jarman  Alexandre M. Tartakovsky 《Advances in water resources》2011,34(5):659-670

Moment equation methods are popular and powerful tools for modeling transport processes in randomly heterogeneous porous media, but the application of these methods to advection-dispersion equations often leads to erroneous oscillations. Perturbative methods, required to close systems of moment equations, become inaccurate for large perturbations; however, little quantitative theory exists for determining when this occurs for advection-dispersion equations. We consider three different methods (asymptotic approximation, Eulerian truncation, and iterative solution) for closing and solving advection-dispersion moment equations describing transport in stratified porous media with random permeability. We obtain approximate analytical expressions for time above which the asymptotic approximation to the mean diverges, in particular quantifying the impact that dispersion has on delaying—but not eliminating—divergence. We demonstrate that Eulerian truncation and iterative solution methods do not eliminate divergent behavior either. Our divergence criteria provide a priori estimates that signal a warning to the practitioner of stochastic advection-dispersion equations to carefully consider whether to apply perturbative approaches.  相似文献   

Tensionless–frictionless interaction of flexible annular foundation with a transversely isotropic multi‐layered half‐space          下载免费PDF全文

Morteza Eskandari‐Ghadi  Ghasem Gorji‐Bandpey  Azizollah Ardeshir‐Behrestaghi  Seyed Masoud Nabizadeh 《国际地质力学数值与分析法杂志》2015,39(2):155-174

A transversely isotropic multi‐layered half‐space, with axis of material symmetry perpendicular to the free surface, supports a flexible either annular or solid circle foundation. The contact area of the foundation and the half‐space is considered to be both frictionless and tensionless. The foundation is assumed to be affected by a vertical static axisymmetric load. Detailed analysis of the interaction of these two systems with different thickness of layers is the target of this paper. With the use of ring load Green's functions for both the foundation and the continuum half‐space, an integral equation accompanied with some inequalities is introduced to model the complex BVP. With the incorporation of ring‐shape FEM, we are capable of capturing both regular and singular solution smoothly. The validity of the combination of the analytical and numerical method is proved with comparing the results of this paper with a number of benchmark cases of both linear and nonlinear interaction of circular and annular foundation with half‐space. Some new illustrations are presented to portray the aspect of the anisotropy and layering of the half‐space. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

One‐dimensional dynamics of saturated incompressible porous media: analytical solutions and influence of inertia terms          下载免费PDF全文

Yunpeng Zhang  Dorival M. Pedroso  Wolfgang Ehlers 《国际地质力学数值与分析法杂志》2016,40(18):2489-2513

The complexity of formulations for the hydromechanical coupled mechanics of porous media is typically minimised by simplifying assumptions such as neglecting the effect of inertia terms. For example, three formulations commonly employed to model practical problems are classified as fully dynamic, simplified dynamic and quasi‐static. Thus, depending on the porous media conditions, each formulation will have advantages and limitations. This paper presents a comprehensive analysis of these limitations when solving one‐dimensional fully saturated porous media problems in addition to a new solution that considers a more general loading situation. A phase diagram is developed to assist on the selection of which formulation is more appropriate and convenient regarding particular cases of porosity and hydraulic conductivity values. Non‐dimensional formulations are proposed to achieve this goal. Results using the analytical solutions are compared against numerical values obtained with the finite element method, and the effect of porosity is investigated. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

缺少控制点的星载SAR遥感影像对地目标定位   总被引：4，自引：2，他引：2  

袁修孝  吴颖丹 《武汉大学学报(信息科学版)》2010,(1)

从距离和多普勒方程出发,构建了无需地面控制点的直接对地目标定位模型,推导了缺少控制点时的精化轨道参数及成像几何参数等的数学模型。经过对北京某地区一景ENVISAT ASAR影像进行直接对地目标定位,获得了实地上±170.966 m(约±8.7像素)的平面精度;利用单个地面控制点对星载SAR影像的定向参数实施调整后,对地目标定位平面精度提高到±54.665 m(约±2.8像素),控制点数目增加到4个时,对地目标定位平面精度接近±2像素。结果显示,对困难地区采用星载SAR遥感影像对地目标定位具有很好的应用前景。  相似文献   

Effect of bed surface roughness on longitudinal dispersion in artificial open channels     

Marcus Schulz  Jan Priegnitz  Jörg Klasmeier  Stefan Heller  Stefan Meinecke  Michael Feibicke 《水文研究》2012,26(2):272-280

In several empirical and modelling studies on river hydraulics, dispersion was negatively correlated to surface roughness. In this study, it was aimed to investigate the influence of surface roughness on longitudinal dispersion under controlled conditions. In artificial flow channels with a length of 104 m, tracer experiments with variations in channel bed material were performed. By use of measured tracer breakthrough curves, average flow velocity, mean longitudinal dispersion, and mean longitudinal dispersivity were calculated. Longitudinal dispersion coefficients ranged from 0·018 m² s^?1 in channels with smooth bed surface up to 0·209 m² s^?1 in channels with coarse gravel as bed material. Longitudinal dispersion was linearly related to mean flow velocity. Accordingly, longitudinal dispersivities ranged between 0·152 ± 0·017 m in channels with smooth bed surface and 0·584 ± 0·015 m in identical channels with a coarse gravel substrate. Grain size and surface roughness of the channel bed were found to correlate positively to longitudinal dispersion. This finding contradicts several existing relations between surface roughness and dispersion. Future studies should include further variation in surface roughness to derive a better‐founded empirical equation forecasting longitudinal dispersion from surface roughness. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems     

陈金兵  耿献国  乔志军 《海洋学报(英文版)》2010,29(9)

On the tangent bundle TS^N-1 of the unit sphere S^N-1, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel--Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.  相似文献   

利用控制点三维信息标定机载双天线干涉SAR参数   总被引：1，自引：1，他引：0  

张薇  向茂生  吴一戎 《测绘学报》2010,39(4):370-377

采用基于敏感度方程的方法,研究基于三维重建模型下的机载双天线干涉SAR系统的干涉参数定标问题.干涉参数定标是生成高精度数字高程模型的关键.本文修正了Madsen提出的干涉SAR三维重建的视向量正交分解算法,采用电磁波波前的球面波模型,加入了载机的姿态旋转,构建一种新的干涉SAR三维重建模型.利用各干涉参数对控制点三维信息的不同的敏感性,提出分别利用地面控制点三维信息,对各干涉参数进行定标.并利用中国科学院电子学研究所自主设计、研制的机载干涉SAR系统数据,进行定标处理实验验证.  相似文献   

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor   总被引：2，自引：1，他引：1  

王大国  邹志利  谭国焕  刘霞 《中国海洋工程》2010,24(1):41-56

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor.The domain is divided into an inner domain and an outer domain.The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations.The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions.Along the interface boundaries between the inner domain and the outer domain,the volume flux is assumed to be continuous and the wave pressures are equal.Relevant physical experiment is conducted to validate the present model.It is shown that the numerical results agree with the experimental data.Compared with the coupled model with the flow in the inner domain governed by the Laplace equation,the present coupled model is more efficient and its solution procedure is more simple,which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.  相似文献   

Effective block diagonal preconditioners for Biot's consolidation equations in piled‐raft foundations     

K. B. Chaudhary  K. K. Phoon  K. C. Toh 《国际地质力学数值与分析法杂志》2013,37(8):871-892

The finite element (FE) simulation of large‐scale soil–structure interaction problems (e.g. piled‐raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi‐minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over‐relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled‐raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over‐relaxation, and ILU preconditioners in simulating piled‐raft foundations. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

The tripole: A new coherent vortex structure of incompressible two-dimensional flows     

Lorenzo M. Polvani  Xavier J. Carton 《地球物理与天体物理流体动力学》2013,107(1-4):87-102

Abstract

Using a contour dynamical algorithm, we have found rotating tripolar V-state solutions for the inviscid Euler equations in two-dimensions. We have studied their geometry as a function of their physical parameters. Their stability was investigated with the aid of contour surgery, and most of the states were found to be stable. Under finite-amplitude perturbations, tripoles are shown to either fission into two asymmetric dipoles or to evolve into a shielded axisymmetric vortex, demonstrating the existence of two new ‘‘reversible transitions'’ between topologically distinct coherent vortex structures. These dynamical results are confirmed by pseudo-spectral simulations, with which we also show how continuous tripolar long-lived coherent vortex structures can be generated in a variety of ways.  相似文献