統一坐標系下的計算流體力學方法

統一坐標系下的計算流體力學方法

图书基本信息
出版时间:2012-2
出版社:科學出版社
作者:許為厚(Wai How Hui) 著
页数:189
书名:統一坐標系下的計算流體力學方法
封面图片
統一坐標系下的計算流體力學方法

内容概要
  本書是運用大規模數值計算來解決流體的運動問題。眾所周知,在流體計算中,一個給定流場的數值解是該流場的流動狀態在為其設定的坐標中的體現。計算流體力學通常使用的兩個坐標系,即歐拉坐標系和拉格朗日坐標系,既有優點又有不足。歐拉方法相對簡單,但是其不足在于︰(a)對接觸間斷的分辨率不足;(b)在流體計算之前先要生成貼體坐標。相反地,拉格朗日方法很好地分辨出接觸間斷(包括物質介面和自由面),但它的缺點在于︰(a)氣體動力方程不能寫成守恆型偏微分方程的形式,使得數值計算復雜和缺乏唯一性;(b)由于網格扭曲導致計算中斷。因此,計算流體力學的基本問題除了深刻理解物理流動之外,同時也要尋找"最優的"坐標系。統一坐標系方法是《統一坐標系下的計算流體力學方法》第一作者許為厚教授在前人坐標變換的基礎上的進一步發展,並在與其同事多年的合作中建立起來的。在計算流體力學的研究中尋找"最優的"坐標系肯定還會繼續下去,目前為止,統一坐標系可較好地結合前兩種坐標系的優點,避免它們的不足。例如,統一坐標系可以通過計算自動生成網格,而且網格速度也可以考慮加入避免網格大變形的"擴散"速度。《統一坐標系下的計算流體力學方法》首先回顧了一維和多維計算流體力學中的歐拉、拉格朗日以及ALE(Arbitrary-Lagrangian-Eulerian)方法的優缺點以及各種移動網格方法,然後系統介紹了統一坐標法,用一些具體的算例闡明它和現有方法之間的關系。
书籍目录
Chapter 1 Introduction
1.1 CFD as Numerical Solution to Nonlinear Hyperbolic PDEs
1.2 Role of Coordinates in CFD
1.3 Outline of the Book
References
Chapter 2 Derivation of Conservation Law Equations
2.1 Fluid as a Continuum
2.2 Derivation of Conservation Law Equations in Fixed
Coordinates
2.3 Conservation Law Equations in Moving Coordinates
2.4 Integral Equations versus Partial Differential Equations
2.5 The Entropy Condition for Inviscid Flow Computation
References
Chapter 3 Review of Eulerian Computation for 1-D Inviscid
Flow
3.1 Flow Discontinuities and Rankine-Hugoniot Conditions
3.2 Classification of Flow Discontinuities
3.3 Riemann Problem and its Solution
3.4 Preliminary Considerations of Numerical Computation
3.5 Godunov Scheme
3.6 High Resolution Schemes and Limiters
3.7 Defects of Eulerian Computation
References
Chapter 4 I-D Flow Computation Using the Unified Coordinates
4.1 Gas Dynamics Equations Based on the Unified Coordinates
4.2 Shock-Adaptive Godunov Scheme
4.3 The Use of Entropy Conservation Law for Smooth Flow
Computation
4.4 The Unified Computer Code
4.5 Cure of Defects of Eulerian and Lagrangian Computation by the
UC Method
4.6 Conclusions
References
Chapter 5 Comments on Current Methods for Multi-Dimensional Flow
Computation
5.1 Eulerian Computation
5.2 Lagrangian Computation
5.3 The ALE Computation
5.4 Moving Mesh Methods
5.5 Optimal Coordinates
References
Chapter 6 The Unified Coordinates Formulation of CFD
6.1 Hui Transformation
6.2 Geometric Conservation Laws
6.3 Derivation of Governing Equations in Conservation Form
References
Chapter 7 Properties of the Unified Coordinates
7.1 Relation to Eulerian Computation
7.2 Relation to Classical Lagrangian Coordinates
7.3 Relation to Arbitrary-Lagrangian-Eulerian Computation
7.4 Contact Resolution
7.5 Mesh Orthogonality
7.6 Unified Coordinates for Steady Flow
7.7 Effects of Mesh Movement on the Flow
7.8 Relation to Other Moving Mesh Methods
7.9 Relation to Mesh Generation and the Level-Set Function
Method
References
Chapter 8 Lagrangian Gas Dynamics
8.1 Lagrangian Gas Dynamics Equations
8.2 Weak Hyperbolicity
8.3 Non-Equivalency of Lagrangian and Eularian Formulation
References
Chapter 9 Steady 2-D and 3-D Supersonic Flow
9.1 The Unified Coordinates for Steady Flow
9.2 Euler Equations in the Unified Coordinates
9.3 The Space-Marching Computation
9.4 Examples
……
Chapter 10 Unsteady 2-D and 3-D Flow Computation
Chapter 11 Viscous Flow Computation Using Navier-Stokes
Equations
Chapter 12 Applications of the Unified Coordinates to Kinetic
Theory
Chapter 13 Summary
Appendix A Riemann Problem for 1-D Flow in the Unified
Coordinate
Appendix B Computer Code for 1-D Flow in the Unified Coordinate

章节摘录
插圖︰(2) Practical methods for computing solutions with shock discontinuities aredeveloped: the artificial viscosity method of von Neumann and Richtmyer whichsmears shock discontinuities[4]; the Godunov method which reduces the generalinitial value problem to a sequence of Riemann problems with cell-averaging data[5] ;the Glimm random choice method which also reduces the general initial valueproblem to a sequence of Riemann problems but with data of randomly chosenrepresentative states[6, 7]; and the shock-fitting (front tracking) method[S].  Thelast two methods are not easily extended to the three-dimensional flow.(3) A very important discovery was made by Lax and Wendroff[9] that in orderto numerically capture shock discontinuities correctly, the governing PDE shouldbe written in conservation form to begin with.  This is easily done in Euleriancoordinates (in any dimensions) and also for one-dimensional flow in Lagrangiancoordinates. But for a long time, it was not known how to use Lagrangian coordinates to write the governing PDEs for multidimensional flows in conservation form.This problem was solved by Hui et al.
编辑推荐
《統一坐標系下的計算流體力學方法》編輯推薦︰This book reviews the relative advantages and drawbacks of Eulerian and Lagrangiancoordinates as well as the Arbitrary Lagrangian-Eulerian (ALE) and various moving meshmethods in Computational Fluid Dynamics (CFD) for one and multidimensional flows.It then systematically introduces the unified coordinate approach to CFD, illustrated withnumerous examples and comparisons to clarify its relation with existing approaches. Thebook is intended for researchers and practitioners in the field of Computational Fluid Dynamics.Emeritus Professor Wai-How Hui and Professor Kun Xu both work at the Department ofMathematics of the Hong Kong University of Science & Technology, China.


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评论与打分
  •     要看的,全英的,有點意料之外
  •     本書總體來說不錯,是兩位在計算流體力學方面的權威專家著的,特別是建立的統一坐標系用于解決不溶的兩相和多相問題的解決很有用。