《重大裝備中問題驅動的套用數學理論和方法》內容涉及葉輪機械內部流動、渦輪增壓、柴油發動機熱力氣動循環、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繫，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。
基本介紹
- 書名：重大裝備中問題驅動的套用數學理論和方法
- 出版社：西安交通大學出版社
- 頁數：664頁
- 開本：16
- 品牌：西安交通大學出版社
- 作者：李開秦
- 出版日期：2008年6月1日
- 語種：簡體中文
- ISBN：7560527469, 9787560527468
內容簡介,圖書目錄,文摘,序言,
內容簡介
《重大裝備中問題驅動的套用數學理論和方法》由西安交通大學出版社出版。
圖書目錄
A．葉輪機械、柴油發動機、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
無界區域上非自治Navier—Stokes方程的一致吸引子及其維數估計
非光滑區域上非自治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 ofDislocation of Crystals
TB點計算的一個分裂疊代方法
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的一步牛頓疊代法
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
無界區域上非自治Navier—Stokes方程的一致吸引子及其維數估計
非光滑區域上非自治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 ofDislocation of Crystals
TB點計算的一個分裂疊代方法
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的一步牛頓疊代法
文摘
OptimalShapeDesignforBlade's
SurfaceofanImpellerViatheNavier-StokesEquations1INTRODUCTION
ShapeDesignforBlade'sSurfaceofaImpellerisdrivenbytheneedforimprovingperformanceandreliability.Inthispaper,wetrytoproposeaprincipleforafullymathematicaldesignforthesurfaceofthebladeinanimpeller.Weshallapplyoptimalcontroltechniquestofindandoptimalshapebyminimizingafunctionalproposedbyus.PioneeringworkonoptimalshapedesignfortheNavier-Stokes（N-S）equationswascarriedoutbyPironneau,whereattemptsweremadeatdeterminingaminimumdragprofilesubmergedinahomogeneous,steady,viscousfluid.GunzburgerandKimstudiedatwodimensionalchannelflowofastationary,incompressible,viscousfluidtodeterminetheshapeofabumponapartoftheboundarythatminimizedtheviscousdragandshowedtheexistenceofoptimalsolutions.Ton,extendedtheworktoaplanenonstationaryflow.Bynow,manyauthorshavediscussedthecontrolproblemofN-Sequationswhichcanbeusedtotheshapedesigninincompressibleviscousflow.
SurfaceofanImpellerViatheNavier-StokesEquations1INTRODUCTION
ShapeDesignforBlade'sSurfaceofaImpellerisdrivenbytheneedforimprovingperformanceandreliability.Inthispaper,wetrytoproposeaprincipleforafullymathematicaldesignforthesurfaceofthebladeinanimpeller.Weshallapplyoptimalcontroltechniquestofindandoptimalshapebyminimizingafunctionalproposedbyus.PioneeringworkonoptimalshapedesignfortheNavier-Stokes（N-S）equationswascarriedoutbyPironneau,whereattemptsweremadeatdeterminingaminimumdragprofilesubmergedinahomogeneous,steady,viscousfluid.GunzburgerandKimstudiedatwodimensionalchannelflowofastationary,incompressible,viscousfluidtodeterminetheshapeofabumponapartoftheboundarythatminimizedtheviscousdragandshowedtheexistenceofoptimalsolutions.Ton,extendedtheworktoaplanenonstationaryflow.Bynow,manyauthorshavediscussedthecontrolproblemofN-Sequationswhichcanbeusedtotheshapedesigninincompressibleviscousflow.
序言
重大裝備中問題驅動的套用數學研究很受國家的重視和提倡，也起數學界和工程界極大的關注。重大裝備中問題驅動的套用數學研，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，Friedmann教授撰寫《工業套用數學》叢書時，走遍美國、日本和歐洲10多個工廠和科研單位。日本岩波出版社20世紀60年代出版的立用數學》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、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學問題。反應了作者研究問題的過程建立數學模型，探討數學方法和進行數學分析，最後到研製相關軟。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，並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。
