| 国际上很权威的作者，该书的学科覆盖面很广。可供研究生及科研人员阅读。本书首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精确性和效率，指出大雷诺数情形下精确计算流的方法；特别讨论了稳定性分析，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方法；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叙率格式加以克服。简要介绍了运用克洛夫子空间理论和多重网格加速的有效的解的迭代方法。 |
| 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 ZTurbulence 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 differenial 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 …… 6. The incompressible Navier-Stokes equations 7. Iterative methods 8. The shallow-water equations 9. Scalar conservation laws 10. The Euler equations in one space dimension 11. Discretization in general domains 12. Numerical solution of the Euler equations in general domains 13. Numerical solution of the Navier-Stokes equations in general domains 14. Unified methods for computing incompressible and compressible flow References Index |
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