重大裝備中問題驅動的應用數(shù)學理論和方法

前言

　　重大裝備中問題驅動的應用數(shù)學研究很受國家的重視和提倡，也起數(shù)學界和工程界極大的關注。重大裝備中問題驅動的應用數(shù)學研，是一個多學科交叉的研究領域，需要有自然科學、計算機科學和數(shù)知識，同時還要對實際問題的背景有所了解。美國科學院院士，F(xiàn)riedmann教授撰寫《工業(yè)應用數(shù)學》叢書時，走遍美國、日本和歐洲10多個工廠和科研單位。日本巖波出版社20世紀60年代出版的立用數(shù)學》叢書的作者們，也是如此。這本文集，收集了作者從70年代到現(xiàn)在有關此方面的研究成果和術論文。其中包括葉輪機械內部流動及葉片設計、柴油機熱力氣動環(huán)、薄壁構件及殼體理論方法、軸承潤滑、核反應堆物理及核電站、重機械等技術課題中提出的數(shù)學問題。反應了作者研究問題的過程建立數(shù)學模型，探討數(shù)學方法和進行數(shù)學分析，最后到研制相關軟。在80年代．錢令希院士，錢偉長院士在給作者的信中就十分欣賞種研究方法和風格，并且主張應該加以提倡。本書可對從事這方面究或有興趣的讀者提供參考。

內容概要

本書內容涉及葉輪機械內部流動、渦輪增壓、柴油發(fā)動機熱力氣動循環(huán)、薄壁構造和殼體理論、軸承潤滑、核反應堆和核電站運行、Navier—Stokes方程理論和建立在近似慣性流形基礎上的算法和維數(shù)分裂算法、非線性問題分歧理論和算法等等，這些問題與工程問題有緊密聯(lián)系，可以為從事相關技術問題研究的讀者或在校的研究生提供參考。

書籍目錄

A．葉輪機械、柴油發(fā)動機、殼體、軸承潤滑和地球物理流動  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  柴油發(fā)動機排氣壓力波計算  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．近似慣性流形和Naviev-Stokes方法的慣性算法  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    時滯慣性流形及近似時滯慣性流形族  N—S方程一般近似慣性流形構造和逼近  N0nlinear Galerkin Method for Navier—Stokes Equations with Stream Form  加罰N—S方程的有限元非線性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   無界區(qū)域上非自治Navier—Stokes方程的一致吸引子及其維數(shù)估計  非光滑區(qū)域上非自治Navier—Stokes方程非齊邊界問題的吸引子  The Stability of Navier—Stokes Equations and the Estimation of Its  Attractor Dimension  C．外部問題的邊界積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點計算的一個分裂迭代方法  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方程的非奇異解分支的譜Galerkin逼近  求解Navier—Stokes方程的非退化轉向點的擴充系統(tǒng)的一步牛頓迭代法

章節(jié)摘錄

　　OptimalShapeDesignforBlades　　SurfaceofanImpellerViatheNavier-StokesEquations1INTRODUCTION　　ShapeDesignforBladesSurfaceofaImpellerisdrivenbytheneedforimprovingperformanceandreliability.Inthispaper,wetrytoproposeaprincipleforafullymathematicaldesignforthesurfaceofthebladeinanimpeller.Weshallapplyoptimalcontroltechniquestofindandoptimalshapebyminimizingafunctionalproposedbyus.PioneeringworkonoptimalshapedesignfortheNavier-Stokes（N-S）equationswascarriedoutbyPironneau,whereattemptsweremadeatdeterminingaminimumdragprofilesubmergedinahomogeneous,steady,viscousfluid.GunzburgerandKimstudiedatwodimensionalchannelflowofastationary,incompressible,viscousfluidtodeterminetheshapeofabumponapartoftheboundarythatminimizedtheviscousdragandshowedtheexistenceofoptimalsolutions.Ton,extendedtheworktoaplanenonstationaryflow.Bynow,manyauthorshavediscussedthecontrolproblemofN-Sequationswhichcanbeusedtotheshapedesigninincompressibleviscousflow.

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