基本信息
出版社: 科學出版社; 第1版 (2012年3月1日)外文書名:Computational Fluid Dynamics Based on the Unified Coordinates
精裝: 189頁
正文語種: 英語
開本: 16
ISBN: 9787030323194
條形碼: 9787030323194
商品尺寸: 23.6 x 15.8 x 1.6 cm
商品重量: 422 g
內容簡介
《統一坐標系下的計算流體力學方法》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，但是其不足在於：（a）對接觸間斷的解析度不足；（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），但它的缺點在於：（a）氣體動力方程不能寫成守恆型偏微分方程的形式，使得數值計算複雜和缺乏唯一性；（b）由於格線扭曲導致計算中斷。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格線，而且格線速度也可以考慮加入避免格線大變形的"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格線方法，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係。目錄
Chapter 1 Introduction1.1 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
