数值流形方法及其与耦合方法的比较     

张勇慧  平扬  刘明智 《岩土力学》2004,25(Z2):93-96

介绍了数值流形方法的基本原理,讨论了数学覆盖、物理覆盖、权函数和位移函数的概念,比较了该方法与DDA和FEM的耦合方法在对一维特性函数逼近的精确度,并用这两种方法模拟了地下放顶煤开挖的过程,最后的结果显示数值流形方法具有较好的相容性和精确度.  相似文献   

Barrier destruction and Lagrangian predictability at depth in a meandering jet     

G. -C. Yuan  L. J. Pratt  C. K. R. T. Jones 《Dynamics of Atmospheres and Oceans》2002,35(1)

Numerical simulations of a jet with large amplitude meanders are used to explore chaotic advection processes and underlying geometry changes as functions of the ambient potential vorticity gradient β. Variations in β in the 2D model qualitatively simulate changes in depth in 3D, surface-intensified jets such as the Gulf Stream. As β is reduced, corresponding to motion on increasingly deep isopycnal surfaces, a number of geometrical transitions take place in the flanges and across the core of the jet. The most important is a joining (or separatrix reconnection) of heteroclinic cat’s eyes structures lying to the north and south of the jet core. The jet core acts as a barrier to transport, but this barrier is breached when the cat’s eyes merge. The subsequent chaotic transport across the jet is demonstrated by calculations of effective invariant manifolds (EIMs) originating in hyperbolic regions to the north and south of the core. Destruction of the central barrier occurs as β is lowered through a narrow window W about β=0 and is marked by transitions form a meandering jet through a vortex street with no central meandering flow to a vortex street with a retrograde meander. Such small values of β are deemed reasonable in view of measurements of low potential vorticity gradients in the deep Gulf Stream. The strength of the central barrier for β outside W is tested by varying β about a mean value β₀ and detecting the minimum amplitude of fluctuation necessary for destruction of the barrier. It is found that the barrier is stronger for β₀>0, at least by this measure. A striking difference is that, for β<0, some disturbances may destroy the barrier without oscillating across W; whereas for β>0, destruction of the barrier may only occur when β passes through W. Changes in underlying geometry also occur in the flanges of the jet and these changes alter the locations in which fluid is preferentially stirred and mixed. Float trajectories can be regular or irregular depending upon where the instrument is launched and this is demonstrated by plotting trajectories from inside and outside regions of chaotic advection.  相似文献   

数值流形方法及在川滇地区地壳运动研究中的应用(英文)     

Caijun Xu  Changrong Yi  Ting Chen 《地球空间信息科学学报》2008,11(3):157-161

The numerical manifold method （NMM） can calculate the movements and deformations of structures or materials. Both the finite element method （FEM） for continua and the discontinuous deformation analysis （DDA） for block systems are special cases of NMM. NMM has separate mathematical covers and physical meshes： the mathematical covers define only fine or rough approximations; as the real material boundary, the physical mesh defines the integration fields. The mathematical covers are triangle units; the physical mesh includes the fault boundaries, joints, blocks and interfaces of different crust zones on the basis of a geological tectonic background. Aiming at the complex problem of continuous and discontinuous deformation across the Chinese continent, the numerical manifold method （NMM） is brought in to study crustal movement of the Stchuan-Yunnan area. Based on the GPS velocity field in the Sichuan-Yunnan area, a crustal strain and stress field is simulated and analyzed. Moreover, results show that the NMM is a more suitable method than DDA in simulating the movement of the Sichuan-Yunnan area. Finally, a kind of mechanism of crustal motion in the Sichuan-Yunnan area is discussed in the paper.  相似文献   

球面数字空间下的基本拓扑模型     

侯妙乐  赵学胜  陈军 《地理信息世界》2004,2(2):38-43

球面格网数据模型SGDM(Sphere Grid Data Model)具有多分辨率和层次组织的特性,已成为目前构建globe GIS的有效方法之一。但是,目前关于球面定性和定量的相关模型方法,大都建立在球面连续空间之上。为使计算机能有效地进行球面空间数据处理和关系计算,亟需在球面离散空间上建立起一套空间分析模型和相关方法。本文给出了球面数字空间的定义和特性,建立了基于流型的球面数字空间的基本拓扑模型,将Egenhofer等人的4交关系模型推广到球面数字空间。  相似文献   

基于数值流形法的重力坝多裂纹扩展研究     

徐栋栋  杨永涛  郑宏  邬爱清 《岩土力学》2016,37(12):3598-3607

传统数值流形法（NMM）在处理非连续变形问题时,仅限于几何构型不发生破坏的情况。针对这一不足,通过在裂纹尖端附近的物理片上增加用于模拟应力奇异性的增强位移函数,进一步发展了可用于几何构型破坏的扩展的高阶NMM。然后,将其应用到重力坝由连续到非连续的破坏过程分析中。首先,针对一含单裂纹的重力坝模型进行了敏感性分析,结果表明,在不同的扩展长度或网格密度下,其扩展路径基本相同且与文献结果保持一致。进而在此模型基础上又开展了多裂纹扩展分析,结果仅一条主导裂纹发生扩展,与文献结果基本一致。最后,针对印度的Koyna重力坝,通过设置不同的漫顶高度研究了其裂纹扩展路径的变化。结果表明,随着漫顶高度的增大,裂纹扩展路径逐渐趋向于水平方向扩展,而且坝体抵抗破坏的能力逐渐减弱。总体表明,NMM在求解实际工程问题时具有很好的数值稳定性和鲁棒性。  相似文献   

岩体黏弹性蠕变计算的高阶数值流形法研究     

刘建  陈佺 《岩土力学》2012,33(7):2174-2180

数值流形法（numerical manifold method）是一种新型的数值计算方法,已成功应用于岩土工程的诸多领域,但该方法尚未应用于岩土工程蠕变分析。近年来对高阶流形法的研究表明,对复杂的岩土工程问题,使用高阶覆盖函数可明显提高流形法的计算精度。为此,开展了用高阶流形法模拟蠕变的研究,在高阶流形法中引入“时步-初应变”法计算蠕变,以广义开尔文体为基础,推导了相关的计算公式,并编制了相应的计算程序,同时还通过算例,验证了方法的可行性和合理性。结果表明,高阶流形可以方便地与“时步-初应变”法结合用于蠕变计算,可较好地模拟蠕变变形。算例分析表明,在不改变网格密度情况下,仅通过采用高阶覆盖函数,高阶流形法可大幅提高传统流形法的计算精度。  相似文献   

A multiscale manifold method using particle representations of the physical domain     

L. Sun  G. F. Zhao  J. Zhao 《Geomechanics and Geoengineering》2014,9(2):124-132

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数值流形方法中覆盖函数选用的建议   总被引：5，自引：0，他引：5  

彭自强  葛修润 《岩土力学》2004,25(4):624-627

在数值流形方法中,常用的覆盖函数基并非是最佳选择。循着刚度矩阵的形成过程,分析了选用常用覆盖函数时,在非对角元上出现绝对值很大的元素之成因,且发现这会增加刚度矩阵的条件数,尤其是在用刚性弹簧约束位移的情况下,而这在数值流形方法中普遍而基本。建议采用局部化较好的覆盖函数,取代常用的关联于全局坐标的覆盖函数,可显著消除这一情况。建议方式简单明了,程序改动极小,对改善刚度矩阵性态却有很大作用。算例验证了这一建议的合理性,通过比较局部化的覆盖函数及全局性的覆盖函数所形成的刚度矩阵,表明前者形成了较小条件数的刚度矩阵。  相似文献   

高阶流形方法模拟裂纹扩展研究   总被引：10，自引：3，他引：7  

王水林  冯夏庭  葛修润 《岩土力学》2003,24(4):622-625

在物理覆盖上采用一阶覆盖函数（即单元上位移函数为二阶）模拟裂纹扩展,并且基于采用的覆盖函数给出了一种裂纹尖端停留在单元内部的算法,从而,可控制每一步裂纹扩展的长度。该方法可弥补物理覆盖上使用常覆盖函数模拟裂纹扩展时无法准确控制扩展长度的不足。  相似文献   

高维数据非参数密度估计的低维流形代表点法     

王树良  李英  耿晶 《武汉大学学报(信息科学版)》2021,46(1):65-70

非参数核方法由于采用统一的度量标准,在大数据中利用高维样本数据学习时容易遭遇维数灾难问题.挖掘高维空间中的低维几何特性,有助于揭示数据分布的流形结构,进而利用有限样本的高维数据在低维子空间逼近数据的真实分布.基于此,提出一种新的高维数据密度非参数估计的低维流形代表点法,通过从高维空间中挖掘数据分布的几何结构来估计密度....  相似文献