Numerical Simulation of Viscous Cavitating Flow Around A Ship Propeller

弗赖登塔尔弗赖登塔尔2011-05-04 17:14:43| 分类：读书之窗| 标签：|字号大中小订阅弗赖登塔尔﹝H. Freudent弗赖登塔尔﹝H. Freudenthal﹞《做为教育任务的数学》《除草与播种──数学教育科学的前言》《数学结构的教学现象学》汉斯?弗赖登塔尔﹝Hans Freudenthal，1905-1990﹞，荷兰数学家、数学教育家。

本文主要介绍他的三本着作：《作为教育任务的数学》﹝Mathematics as an Educational Task，D. Reidel Publishing Company，1973﹞、《除草与播种─数学教育科学的前言》﹝Weeding and Sowing─Preface to a Science of Mathematical Education. D. Reidel Publishing Company，1978﹞、《数学结构的教学现象学》﹝Didactical Phenomenology of Mathematical Structures，D. Reidel Publishing Company，1983﹞.一、作者介绍汉斯?弗赖登塔尔﹝1905─1990﹞为国际上享有圣名的数学教育权威，荷兰数学家和数学教育家。

他出生于德国，1930年获柏林大学数学博士学位，自1946年起任荷兰乌得勒支﹝Utrecht﹞大学教授，1951年起为荷兰皇家科学院院士，1971─1976年任数学教育研究所所长，他还曾获的柏林大学、爱尔朗根大学、布鲁塞尔大学、多伦多大学及阿姆斯特丹大学的荣誉博士称号。

弗赖登塔尔在数学方面的主要工作领域是拓朴学和李群【辣椒注：在数学中，李群（Lie group）是具有群结构的实流形或者复流形，并且群中的加法运算和逆元运算是栁形中的解析映射。

李群在数学分析、物理和几何中都有非常重要的作用。

同时李群也常被用于人名，在诸多领域均有同名人物】。

关于闭式空泡水洞中洞壁效应的数值模拟1陈鑫， 鲁传敬上海交通大学工程力学系，上海(200240)摘 要：在闭式空泡水洞中，洞壁效应对空泡外形和水动力特性有显著的影响。

本文基于RANS方程，在各向同性Mixture多相流模型的基础上耦合自然空化模型。

采用RNG k-ε湍流模式封闭粘性方程组；采用有限体积法离散控制方程；离散化后的代数方程系统的求解采用基于分离算法的Gauss-Seidel线性方程求解器；并结合“代数”多重网格法加速收敛。

针对给定的带圆盘空化器的水下航行体模型，模拟了不同直径水洞内不同通气量下的定常通气空泡流。

得到了不同直径水洞内的阻塞空化数，与三维圆盘的近似解基本吻合。

发现临界通气率随水洞直径的减小而减小，相同通气率下的空泡尺度和阻力系数随水洞直径的减小而增大，相同通气空化数下不同直径的水洞可能产生尺度差别很大的空泡。

关键词：通气空泡，洞壁效应，阻塞空化数，临界通气率Abstract：In a close cavitation tunnel, the wall effect exerts an influence on the shape and hydrodynamics of cavity. In this paper, based on the RANS equations a natural cavitation model was coupled with the isotropic Mixture multiphase model. The RNG k-ε turbulent model was adopted to close the viscous equations. The finite volume method was employed to discretize the governing equations. The system of discrete equations was solved by Gauss-Seidel linear equation solver on the basis of segregate algorithm. The algebraic multigrid approach was carried out to accelerate convergence. The steady ventilated cavitating flows were simulated in different diameter of water tunnel for a given underwater vehicle model with a disk cavitator. A blocking cavitation number was gained for a water tunnel of different diameter and it is close to the approximate solution for a 3D disk. It was found that the critical ventilation rate falls with decreasing diameter of the water tunnel, the cavity size and drag coefficient are rising with the decrease in diameter of the water tunnel for same ventilation rate, and the cavity size maybe has a big difference in water tunnels of different diameter for same ventilated cavitation number.Key words：ventilated cavitation, wall tunnel, blocking cavitation number, critical ventilation rate 1. 前言虽然水下航行体通常运动在广阔的水域中，但作为分析依据的试验却是在有边壁或自由面的设备中进行的，邻近的固壁边界对于空泡形态和水动力有着显著的影响，即所谓洞壁效应。

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ultimate rangeultimate recoverable reserves ultimate recoveryultimate recovery factor ultimate resistanceultimate resourcesultimate separation ultimate spacing pattern ultimate strainultimate strengthultimate stressultimate systemultimate temperature ultimate temperature rise ultimate tensile strength ultimate tensionultimatumultorultra-ultra deep wellultra filtration membraneultra large crude carrierultra raysultra selective crackingultra-abyssalultra-acid rockultra-acidicultra-acousticsultra-albaniteultrabasicultrabasic complexultrabasic rock ultracentrifugal method ultracentrifugation ultracentrifugeultra-cleanultra-clean chamberultra-deepultradeep diveultra-deep exploration ultraduraluminultraficheultrafilterultrafiltrationultrafine fiber ultraharmonicsultrahigh frequencyultra-high purityultra-high strength steel ultrahigh voltage transformer oil ultra-high-draftultra-high-speed spinning ultrajetultralinearultralongultralong-spaced electric logultralow-frequency oscillator ultralumin ultraluminescence ultramafic rock ultramafiteultramarine ultrametamorphism ultramicroultramicro method ultramicro-analysis ultramicrobalance ultramicrochemistry ultramicro-determination ultramicro-earthquake ultramicrofiche ultramicrofossil ultramicrometer ultramicron ultramicropaleontology ultramicropore ultramicroscope ultramicroscopic ultramicrospectrophotometer ultramicrospectrophotometry ultramicrostructure ultramicrotechnique ultramicrotome ultramicrowave ultramodern ultramylonite ultraoptimeter ultrapaleontology ultraperm ultraperminvar ultraphotometer ultraplankton ultraporcelainultra-pure zinc anode ultrapurification ultrapurityultrasensitive amino acid analyzer ultra-sensitive pressure gauge ultrashort waveultra-slim hole rig ultrasonatorultrasonicultrasonic atomizerultrasonic biasultrasonic casing inspection tool ultrasonic cement analyzer ultrasonic cleanerultrasonic cleaningultrasonic converterultra-sonic defect detector ultrasonic defectoscope ultrasonic 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虚拟烟雾模拟摘要：在这篇文章中，我们提出一种计算机图形应用领域中新的烟雾数值模拟的方法，即使用非粘性的欧拉方程作为烟雾的物理模型，这是一种稳定、快速并有很少的数值耗散的方法。

相比采用N-S方程的物理方法，它更加适合气体建模，并且计算量要小得多。

此外，我们还引入物理上一致的漩涡限制来保证烟雾在粗糙网格（相比使用更精细的计算流体力学文献中网格）上小尺度特征的模拟，并正确地处理与运动物体相互作用。

关键词：烟雾；计算流体动力学；Navier-Stokes方程；欧拉方程；半拉格朗日方法；稳定流体；漩涡限制；participating media参与媒体Ronald Fedkiw, Jos Stam and Henrik Wann Jensen, "Visual Simulation of Smoke", In SIGGRAPH 2001 Conference Proceedings, Annual Conference Series, August 2001, 15-221.引言：由于气体如烟雾的运动是极其复杂并难以捉摸的，所以模拟自然现象如烟雾等，在计算机图形领域仍然是一个具有挑战性的问题。

可视化的烟雾模型，广泛应用于包括特殊效果和互动游戏等相关行业领域，一个好的模型应该易于使用和生成并且具有很强的现实意义。

很显然，烟雾和气体的造型在其它工程领域也是非常重要的。

更普遍地讲，计算流体动力学广泛应用于气体和其他液体，例如水的模拟。

可直到最近，计算机图形学的研究人员才开始从大量的CFD文献中挖掘可以用于或修改计算机图形应用的方法。

不幸的是，目前的烟雾模型不是太缓慢，就是受到过多的数值耗散。

在本文中，我们采用CFD文献中有关气体如烟雾的动画仿真技术，提出了一种稳定、快速且没有过多数值耗散的模型，它使用了一种相对粗糙的网格，来生成复杂的滚动烟雾动画。

1.1 以往工作在过去的二十年里，烟雾及其它气体现象的建模，在计算机图形领域一直受到广泛关注。

基于有限元方法的陀螺仪的盘型制动系统的尖叫分析作者：Jaeyoung Kang【摘要】本文对一辆车的制动系统中旋转阀瓣接触两个固定垫的动力失稳性进行了研究。

在现行的近似几何中，盘被有限元分析法以帽盘型结构为模型。

从参考坐标系和移动坐标系见的坐标变换，对盘和垫之间的接触运动学进行了阐述。

通过引入统一的二维网的方法来构造阀瓣相应的陀螺矩阵。

陀螺仪的非保守性制动系统的动力不稳定性是对系统参数的数值预测。

结果表明, 尖叫声倾向于转速，转速取决于参与尖叫声模式下的振动模式。

而且,它强调摩擦系数的负斜率对在盘的面内扭转模式下产生尖叫声起着至关重要的作用。

【关键词】陀螺仪；盘型制动；制动尖叫；耦合模式1.介绍盘式制动尖叫已经被许多学者研究了数十年。

通过对尖叫机械的研究积累了许多有价值的信息。

Kinkaid等[1]提供了关于各种盘型制动尖叫研究的概述。

Ouyang 等[2]发行了以汽车盘型制动尖叫的数值分析为集中研究的评论性文章。

他们显示一个主要研究制动尖叫的方法，是线性稳定分析。

从线性化的运动微分方程来看,真正的部分特征值被计算出来，用于决定均衡的稳定性。

在文献中，有两个关于线性尖叫分析的主要方向：静态平稳的复杂特征值分析——滑动平稳[3–8]和旋转制动系统的稳定性分析[9–12,14]。

固定盘和垫的静态的滑动稳定的稳定性分析提供尖叫原理作为频繁摩擦领域里的合并模式的特性。

Huang等[6]使用本征值摄动法发展必要的条件没有直接的本征结果。

Kang等[7]推导了盘对之间的合并模式的封闭解。

由于固定盘假设,有限元(FE)方法被容易地应用于上面提到的评论性文章[2]. 同样的，Cao 等[13]从一个有移动垫和固定盘的FE盘型制动模型模型研究了移动荷载效应，因此,陀螺仪的影响被忽视了。

Giannini等[15,16]验证其合并模式行为,通过使用实验尖叫频率作为尖叫开始。

另一方面，旋转盘型制动的稳定性已经调查了分析的方法。

毕业论文题目：二维伊辛模型的蒙特卡罗数值模拟二〇一一年五月目录摘要........................................................... .. (1)Abstract............................................. .. (2)第一章引言 (3)第二章伊辛模型 (4)2.1 伊辛模型的意义 (4)2.2 伊辛模型的历史与发展 (4)2.3 二维伊辛模型的基本结构 (5)第三章蒙特卡罗方法............................................. (6)3.1 蒙特卡罗方法的产生与发展 (6)3.2 蒙特卡罗方法的基本思想 (6)3.3 文中采用蒙特卡罗方法时用到的的基本理论 (7)第四章模拟的理论和过程 (8)4.1 计算理论........................................................ . (8)4.2 模拟过程....................................................... .. (9)第五章数据分析和讨论 (10)参考文献....................................................... . (14)附录....................................................... (15)致谢....................................................... (19)二维伊辛模型的蒙特卡罗数值模拟摘要：本文主要介绍应用蒙特卡罗方法对二维伊辛模型进行数值模拟的基本思路和方法，然后具体应用Fortran语言进行数值模拟的过程。

文中首先介绍了伊辛模型对解决相变问题的意义及其历史与发展，然后介绍了蒙特卡罗方法的产生与发展及其基本内容和思想，最后具体应用计算机Fortran语言用蒙特卡罗方法对二维伊辛模型的相关物理量进行数值模拟的方法和过程，并对所得数据进行分析和讨论。

cavalieri原理Cavalieri原理，也被称为齐次化原理，是数学中常用的一个原理，用于解决平面几何题和立体几何题。

它的发现者是17世纪意大利数学家Bonaventura Cavalieri，他的这一发现被认为是微积分学的萌芽之一Cavalieri原理的核心思想是：如果两个立体图形在任意平行切割面上的截面面积相等，那么这两个立体图形的体积也相等。

这意味着，两个平行且具有相同截面的立体图形，在无穷小切割面上的截面面积应该是相等的。

这个原理的证明是基于微积分的概念，通过对密度积分的方法来推导。

理解Cavalieri原理的一种直观的方式是通过三维实体与平面截面的关系进行比较。

例如，我们可以想象一个圆锥体和一个圆柱体，它们具有相同的截面面积。

根据Cavalieri原理，如果我们将这两个实体在无穷小切割面上切割成无数个薄片，并且每个切割面的截面积相等，那么这两个实体的体积也相等。

在应用Cavalieri原理时，我们可以利用它来解决各种几何问题。

一个典型的应用是计算复杂几何体的体积，特别是当我们没有直接测量或求解其解析表达式的方法时。

通过将几何体与我们已知的几何体进行比较，我们可以使用Cavalieri原理来确定形状相似的几何体的体积。

此外，Cavalieri原理还有一些推论和应用。

例如，如果两个实体的高度相等，但它们的截面面积不同，那么它们体积的比例将等于其截面面积的比例。

这个推论可以用于解决一些实际问题，如计算两个不同形状的容器中液体的体积比例。

Cavalieri原理还可以用于计算平面内的曲线的长度。

通过将曲线切割成无穷多个小线段，并在每个小线段上测量长度，我们可以通过Cavalieri原理得到曲线的总长度。

总而言之，Cavalieri原理是一个强大的工具，可以应用于解决平面几何和立体几何中的各种问题。

它通过将几何图形切割成无穷多的截面，并比较这些截面的面积来推导几何图形的体积和长度。

通过理解和应用Cavalieri原理，我们可以更好地理解和解决各种几何问题。

当代艺点 MODERN ART CLASS皮埃尔·于热，《动物园存储器5》，2011年，玻璃池，过滤系统，树脂面具，寄居蟹，箭蟹和玄武岩作品《动物园存储器5》在水族箱里构建了一个虚拟的海洋生态系统：一只以康斯坦丁·布朗库西（Constantin Brancusi）的雕塑复制品《沉睡的缪斯》（Sleeping Muse）为壳的寄居蟹在水中缓慢移动。

水族馆作为一个汇集全世界不同海洋物种的虚拟自然场域令艺术家着迷。

对艺术家而言，这是一个发生关系分离与断裂的悬置空间。

文：雨田 图：本刊资料库构建人际互动，填补社会裂隙关系艺术（relational art），从字面上理解，是以“关系”作为重心的艺术实践。

是美术实践上所呈现的一种模式或者趋势，它以一种温和的方式让艺术介入社会，艺术家不仅仅是艺术作品的创造者，而更多在于创造一种新型的人与人、人与物、人与空间甚至人与自然的关系。

作为一种新兴的艺术主张，关系艺术在中国，也值得更多元、更深入探索。

创造一种新型的人际网络关系艺术最早于20世纪90年代由法国艺术评论家尼可拉·布西欧( Nicolas Bourriaud) 针对大量出现的互动性艺术、参与性艺术提出的。

当时，互联网与各种新技术蓬勃发展，新一代艺术家受网络和新技术启发，创造了大批具有鲜明时代特色的艺术作品。

1996年，布西欧在法国波尔多当代艺术博物馆策划了一场主题为“交通”的艺术展，展出一批青年艺术家的新锐作品。

包括瓦妮莎·比克罗夫特（Vanessa Beecroft ）、亨利·邦德（Henry Bond ）、毛里齐奥·卡泰兰（Maurizio Cattelan ）、多米尼克·冈萨雷斯-弗尔斯特（Dominique Gonzalez-Foerster ）等人。

这批艺术家日后纷纷名声大噪，成为艺术界的弄潮儿。

在此次展览中，布西欧首次使用“关系艺术”一词来概括参展作品，试图描述90年代基于信息科技的新一代艺术。

拓扑与褶皱——当代前卫建筑的非欧几何实验
李建军
【期刊名称】《新建筑》
【年(卷),期】2010(000)003
【摘要】论述了拓扑几何的概念及主要命题,包括皱褶、纽结与流形.比较了拓扑几何下的建筑审美体系与欧式几何体系下是如何的不同.分析了拓扑几何对当代先锋主义建筑实验、高维建筑空间、甚至拓扑城市的巨大影响.最后,归纳了拓扑学思想下的建筑美学新范式--褶皱美学.
【总页数】5页(P87-91)
【作者】李建军
【作者单位】同济大学建筑与城市规划学院,上海,200092
【正文语种】中文
【中图分类】TU-026
【相关文献】
1.数字时代非欧几何学对当代建筑形体设计的影响简析 [J], 张嘉琦
2.罗巴切夫斯基与非欧几何：纪念非欧几何诞生170周年及罗巴切夫斯基逝世140周 [J], 刘孝贤
3.几何发展中欧氏几何与非欧几何的辩证统一 [J], 娄本平;纪荣芳
4.论当代建筑中非欧几何美学的必然性 [J], 靳铭宇; 刘颖慧
5.从欧氏几何到非欧几何——建筑设计几何法则的转变 [J], 王博涵; 仲美玲
因版权原因，仅展示原文概要，查看原文内容请购买。

闵可夫斯基几何
维纳·闵可夫斯基几何是一种在20世纪初兴起的早期的几何理论，它被用于描述有限的空间，研究在它自身拓扑学上的性质并且允许从拓扑学出发来推断和解释空间，这种几何，以其特有的映射方式定义全局性特征，包括基数，空间正则性和拓扑结构，是一种重要的几何形式。

维纳·闵可夫斯基几何的早期应用围绕着它的拓扑学方面展开，这是由它的独特结构，特别是由它的拓扑结构性质所产生的，同时它又能深刻表达所有拓扑结构与空间特性，例如，在这种几何上概括基数及其向量场。

在互联网时代，维纳·闵可夫斯基几何占据了更重要的地位。

这一几何理论可以非常有效地概括出客观世界中所有系统、网络的特性，同时又能运用其结构信息构建基本模型，并被广泛应用于信息的网络归类，特殊点的检测、信息的传播及演化，以及复杂系统的分析和表达。

它有助于人们对于互联网和它背后的结构及性质有更深的见解，并有助于增强对新信息的な把握。

除此之外，维纳·闵可夫斯基几何还可用于处理具有复杂结构的复杂数据，例如，它可以有效运用于社交网络分析，帮助我们优化聚类及其他复杂信息处理，以及其他复杂信息系统的分析，从而避免使用复杂的线性代数工具或先进数据分析工具。

维纳·闵可夫斯基几何为我们提供了一种非常方便的框架，基于这种框架，我们可以方便地探究网络的特征、特性和结构，也可以深入地解读复杂的数据，以及使用维纳·闵可夫斯基几何驱动的技术来进行高效算法开发、计算机建模和数据分析。

维纳·闵可夫斯基几何是对当今社会信息处理未来的一个期许。

用于图像与视频数字水印技术的视觉模型
叶新友
【期刊名称】《微计算机信息》
【年(卷),期】2010(026)002
【摘要】视觉模型在数字水印技术中有重要的应用,它可以在保持水印不可见性的同时,最大程度的增强水印的鲁棒性.本文就是对应用于图像与视频数字水印技术的视觉模型做一个较为全面的介绍.
【总页数】2页(P190-191)
【作者】叶新友
【作者单位】214122,江苏无锡,江南大学图书馆
【正文语种】中文
【中图分类】TP309
【相关文献】
1.用于图像内容认证的数字水印技术研究 [J], 李东勤
2.一种基于视觉模型的DWT数字水印技术 [J], 周逢朝;檀结庆
3.应用于舌图像的数字水印技术的研究 [J], 胡波;李晓华;沈兰荪
4.用于图像认证的半脆弱数字水印技术综述 [J], 汤文明;李海华
5.数字水印技术应用于遥感图像版权保护的评测标准研究 [J], 陈辉;郭科;郑文峰因版权原因，仅展示原文概要，查看原文内容请购买。

分形几何学是以复杂的、自相似的结构为研究对象的一门学科。

它关注的是那些具有无限细节、无限复杂的图形和形态，并且这些图形和形态在各个尺度上都有相似的特征。

在传统的欧氏几何学中，我们常常使用整数维空间来描述物体的形状和结构。

例如，一个点在一维空间中，一条线在二维空间中，一个平面在三维空间中。

然而，分形几何学却引入了非整数维空间的概念，以更好地描述真实世界中存在的复杂形态。

自相似是分形几何学的一个重要概念。

自相似是指一个物体的局部部分与整体具有相似的形态。

换句话说，无论是放大还是缩小，这个物体的各个部分都具有与整体相似的特点。

自然界中存在着许多自相似的例子，如树枝的分支结构、山脉的起伏、河流的曲线等等。

这些自相似的结构都可以用分形几何学中的数学模型来描述，并得到较好的解释。

分形可以通过一些简单的几何规则来生成。

最经典的分形图形就是科赫曲线。

科赫曲线是一个一维的分形，它由一个线段分割为三等分，然后在中间那一段上重复这个过程。

不断重复这个过程，就可以生成越来越接近科赫曲线的图形。

同样地，科赫雪花可以通过类似的过程生成，只是这次不是在直线上，而是在一个三角形的每条边上进行分割。

这些简单的几何规则在不断重复过程中，产生了无限个趋近于无穷长度的曲线。

分形几何学的研究不仅仅局限于图像和形态的描述，它还可以应用于各个领域。

在自然科学领域，分形几何学被用来研究自然界中的复杂形态，如云朵的形状、植物的分支结构等等。

在医学领域，分形几何学可以应用于分析心电图、肺部CT图像等，为疾病的诊断和治疗提供更准确的数据。

在工程和建筑领域，分形几何学的原理被应用于设计优美的建筑物和城市形态。

在金融领域，分形几何学可以用来分析金融市场的波动性和趋势，为投资者提供参考。

总而言之，分形几何学是一门探索复杂、自相似结构的学科，它在数学、物理、生物学、医学等多个领域都有广泛的应用。

通过研究分形，我们可以更好地理解自然界中的复杂性，同时也能够应用分形的原理来解决实际问题。