内容简介
《计算流体力学原理》是为从事流体计算的研究生、科研人员、工程师和物理学家而写。《国外数学名著系列（影印版）9：计算流体力学原理》先介绍计算流体动力学中的数值方法的现状；运用基本的数学分析，详尽阐述数值计算的基本原理；然后讨论流域和非一致结构化边界适应网格的几何复杂性带来的困难；研究奇异扰动问题的一致性和效率，指出大雷诺数情形下计算流的方法；讨论了稳定性分析，给出在许多实际算法中有价值的稳定性条件，其中某些条件是新的；叙述计算可压缩流和不可压缩流的统一方法；给出了狭窄水漕方程的数值分析；论述了双曲守恒律；讨论了戈杜诺夫阶障碍及如何利用有限斜率格式加以克服。简要介绍了运用克雷洛夫子空间理论和多重网格加速的有效的解的迭代方法。《国外数学名著系列（影印版）9：计算流体力学原理》还包括许多新的文献，以帮助读者迅速了解当前的研究前沿。
目录
Preface
1．The basic equations of fluid dynamics
1．1 Introduction
1．2 Vector analysis
1．3 The total derivative and the transport theorem
1．4 Conservation of mass
1．5 Conservation of momentum
1．6 Conservation of energy
1．7 Thermodynamic aspects
1．8 Bernoulli's theorem
1．9 Kelvin's circulation theorem and potential flow
1．10 The Euler equations
1．11 The convection-diffusion equation
1．12 Conditions for incompressible flow
1．13 Turbulence
1．14 Stratified flow and free convection
1．15 Moving frame of reference
1．16 The shallow-water equations
2．Partial differential equations： analytic aspects
2．1 Introduction
2．2 Classification of partial differential equations
2．3 Boundary conditions
2．4 Maximum principles
2．5 Boundary layer theory
3．Finite volume and finite difference discretization on nonuniform grids
3．1 Introduction
3．2 An elliptic equation
3．3 A one-dimensional example
3．4 Vertex-centered discretization
3．5 Cell-centered discretization
3．6 Upwind discretization
3．7 Nonuniform grids in one dimension
4．The stationary convection-diffusion equation
4．1 Introduction
4．2 Finite volume discretization of the stationary convection diffusion equation in one dimension
4．3 Numerical experiments on locally refined one-dimensional grid
4．4 Schemes of positive type
4．5 Upwind discretization
4．6 Defect correction
4．7 Peclet-independent accuracy in two dimensions
4．8 More accurate discretization of the convection term
5．The nonstationary convection-diffusion equation
5．1 Introduction
5．2 Example of instability
5．3 Stability definitions
5．4 The discrete maximum principle
5．5 Fourier stability analysis
5．6 Principles of von Neumann stability analysis
5．7 Useful properties of the symbol
5．8 Derivation of von Neumann stability conditions
5．9 Numerical experiments
5．10 Strong stability
6．The incompressible Navier-Stokes equations
6．1 Introduction
6．2 Equations of motion and boundary conditions
6．3 Spatial discretization on colocated grid
6．4 Spatial discretization on staggered grid
6．5 On the choice of boundary conditions
6．6 Temporal discretization on staggered grid
6．7 Temporal discretization on colocated grid
7．Iterative methods
7．1 Introduction
7．2 Stationary iterative methods
7．3 Krylov subspace methods
7．4 Multigrid methods
7．5 Fast Poisson solvers
7．6 Iterative methods for the incompressible Navier-Stokes equations
8．The shallow-water equations
9．Scalar conservation laws
10．The Euler equations in one space dimension
11．Discretization in general domains