流体力学建模——不稳定性与湍流(英文)
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作者(以)伊戈尔·盖辛斯基//弗拉基米尔·罗文斯基|
出版社哈尔滨工业大学
ISBN9787576712605
出版时间2024-03
装帧平装
开本其他
定价88元
货号1203275777
上书时间2024-06-30
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目录
Foreword
Preface
1 Mathematical Background
1.1 Dynamical systems
1.1.1 Vector felds and dynamical systems
1.1.2 Critical points in phase space
1.1.3 Higher-order autonomous systems
1.1.4 Dirac delta function
1.1.5 Special functions
1.1.6 Green's function
1.1.7 Boundary and initial value problems
1.2 Asymptotic behavior and stability
1.2.1 Asymptotic expansions
1.2.2 Asymptotic behavior of autonomous systems
1.2.3 Stability of autonomous systems
1.2.4 More on stability
1.3 Bifurcations
1.3.1 Instability and bifurcations
1.3.2 Saddle-node bifurcation
1.3.3 Transcritical and pitchfork bifurcations
1.3.4 Hopf bifurcation
1.3.5 Saddle-node bifurcation of a periodic orbit
1.3.6 Global bifurcation
1.4 Attractors
1.4.1 Chaotic motion and symbolic dynamics
1.4.2 Homoclinic tangles and Smale's horseshoe map
1.4.3 Poincaré return map
1.4.4 Lyapunov's exponents and entropy
1.4.5 Attracting sets and attractors
1.5 Fractals
1.5.1 Local structure of fractals
1.5.2 Operations with fractals
1.5.3 Fractal attractors in dynamical systems
1.6 Perturbations
1.6.1 Regular perturbation theory
1.6.2 Singular perturbation theory
1.7 Elements of tensor analysis
1.7.1 Transformations of coordinate systems
1.7.2 Covariant and contravariant derivatives
1.7.3 Christoffel symbols and curvature tensor
1.7.4 Integral formulas
1.8 Navier-Stokes equations for nonequilibrium gas mixture
1.8.1 Continuity,momentum and energy equations
1.8.2 Closing relations and transport coefficients
1.8.3 Boundary conditions
1.8.4 Deducing Navier-Stokes equation
1.8.5 Existence and uniqueness of solutions of the Navier—Stokes equation
1.8.6 Relativistic Navier—Stokes equation
1.9 Exercises
bliography
内容摘要
本书是一部讲述近代流体力学成果的英文专著，本书认为数学方法和模型是应用数学和理论物理学的分支。本书致力于阐释流体力学建模的相关内容，由四章组成，其中包含大量有用的练习和解决方案。我们在每章末尾的参考书目中提供了相关主题的相对完整的参考资料。
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