重大装备中问题驱动的应用数学理论和方法
2008-6
西安交通大学出版社
李开秦
664
重大装备中问题驱动的应用数学研究很受国家的重视和提倡，也起数学界和工程界极大的关注。重大装备中问题驱动的应用数学研，是一个多学科交叉的研究领域，需要有自然科学、计算机科学和数知识，同时还要对实际问题的背景有所了解。美国科学院院士，Friedmann教授撰写《工业应用数学》丛书时，走遍美国、日本和欧洲10多个工厂和科研单位。日本岩波出版社20世纪60年代出版的立用数学》丛书的作者们，也是如此。这本文集，收集了作者从70年代到现在有关此方面的研究成果和术论文。其中包括叶轮机械内部流动及叶片设计、柴油机热力气动环、薄壁构件及壳体理论方法、轴承润滑、核反应堆物理及核电站、重机械等技术课题中提出的数学问题。反应了作者研究问题的过程建立数学模型，探讨数学方法和进行数学分析，最后到研制相关软。在80年代．钱令希院士，钱伟长院士在给作者的信中就十分欣赏种研究方法和风格，并且主张应该加以提倡。本书可对从事这方面究或有兴趣的读者提供参考。
本书内容涉及叶轮机械内部流动、涡轮增压、柴油发动机热力气动循环、薄壁构造和壳体理论、轴承润滑、核反应堆和核电站运行、Navier—Stokes方程理论和建立在近似惯性流形基础上的算法和维数分裂算法、非线性问题分歧理论和算法等等，这些问题与工程问题有紧密联系，可以为从事相关技术问题研究的读者或在校的研究生提供参考。
A．叶轮机械、柴油发动机、壳体、轴承润滑和地球物理流动 A Geometrical Design Method for Blade’S Surface Shape and General Minimal Surface Optimal Shape Design for Blade’S Surface of an Impeller Via the Navier- Stokes Equations A Dimension Split Method for the 3-D Compressible Navier-Stokes Equations in Turbomachine Mathematical Aspect of Optimal Control Finite Element Method for Navier-Stokes Problems Mathematical Aspect of the Stream—Function Equations of Compressible Turbomachinery Flows and Their Finite Element Approximations Using Optimal Control 柴油发动机排气压力波计算 An Asymptotic Analysis Method for the Linearly Shell Theory 近代梁工程有限元分析 On the Uniqueness of the Unbounded Classical Soultion of the Evolution System Describing Geophysical Flow within the Earth and Its Associated Systems On Existence，Uniqueness and L’-Exponential Starbility for Stationary Solutions to the M HD Equations in Three-Dimensional Domains B．近似惯性流形和Naviev-Stokes方法的惯性算法 A New Approximate Inertial Manifold and Associated Algorithm An AIM and One——Step Newton Method for the Navier——Stokes Equations Fourier Nonlinear Galerkin Method for Navier——Stokes Equations 时滞惯性流形及近似时滞惯性流形族 N—S方程一般近似惯性流形构造和逼近 N0nlinear Galerkin Method for Navier—Stokes Equations with Stream Form 加罚N—S方程的有限元非线性Galerkin方法 A Small Eddy Correction Method for Nonlinear Dissipative Evolutionary Equations Asymptotic Behavior and Time Discretization Analysis for the Non—Stationary Navier—Stokes Problem Convergence and Stability of Finite Element Nonlinear Galerkin Method for the Navier—Stokes Equations Uniform Attractors of Non—Autonomous Dissipative Semilinear Wave Equations 无界区域上非自治Navier—Stokes方程的一致吸引子及其维数估计 非光滑区域上非自治Navier—Stokes方程非齐边界问题的吸引子 The Stability of Navier—Stokes Equations and the Estimation of Its Attractor Dimension C．外部问题的边界积分方程和有限元耦合方法 The Coupling of Boundary Integral and Finite Element Methods for the Navier-Stokes Equations in an Exterior Domain Stokes Coupling Method for the Exterior Flow Part III：Regularity Coupling Method for the Exterior Stationary Navier—Stokes Equations Oseen Coupling Method for the Taylor Expansion Algorithm for the Branching Solution of the Navier Stokes Equations Global Bifurcation and Long Time Behavior of The Volterra—Lotka Ecological Model Existence and Nonexistence of Global Solutions for the Equation of Dislocation of Crystals TB点计算的一个分裂迭代方法 A Splitting Iteration Method for a Simple Corank-2 Bifurcation Problem Bifurcation Solution Branches and Their Numerical Approximations of a Semi—Linear Elliptic Problem with two Parameters On the Solitary Wave Solutions of the CQNLS On Positive Solutions．of the Lotka—Volterra Cooperating Models with Diffusion Navier—Stokes方程的非奇异解分支的谱Galerkin逼近 求解Navier—Stokes方程的非退化转向点的扩充系统的一步牛顿迭代法
OptimalShapeDesignforBlades SurfaceofanImpellerViatheNavier-StokesEquations1INTRODUCTION ShapeDesignforBladesSurfaceofaImpellerisdrivenbytheneedforimprovingperformanceandreliability.Inthispaper,wetrytoproposeaprincipleforafullymathematicaldesignforthesurfaceofthebladeinanimpeller.Weshallapplyoptimalcontroltechniquestofindandoptimalshapebyminimizingafunctionalproposedbyus.PioneeringworkonoptimalshapedesignfortheNavier-Stokes（N-S）equationswascarriedoutbyPironneau,whereattemptsweremadeatdeterminingaminimumdragprofilesubmergedinahomogeneous,steady,viscousfluid.GunzburgerandKimstudiedatwodimensionalchannelflowofastationary,incompressible,viscousfluidtodeterminetheshapeofabumponapartoftheboundarythatminimizedtheviscousdragandshowedtheexistenceofoptimalsolutions.Ton,extendedtheworktoaplanenonstationaryflow.Bynow,manyauthorshavediscussedthecontrolproblemofN-Sequationswhichcanbeusedtotheshapedesigninincompressibleviscousflow.
作者有关重大装备中问题驱动的应用数学的论文汇总，值得参考。