統(tǒng)一坐標(biāo)系下的計(jì)算流體力學(xué)方法

內(nèi)容概要

　　本書(shū)是運(yùn)用大規(guī)模數(shù)值計(jì)算來(lái)解決流體的運(yùn)動(dòng)問(wèn)題。眾所周知，在流體計(jì)算中，一個(gè)給定流場(chǎng)的數(shù)值解是該流場(chǎng)的流動(dòng)狀態(tài)在為其設(shè)定的坐標(biāo)中的體現(xiàn)。計(jì)算流體力學(xué)通常使用的兩個(gè)坐標(biāo)系，即歐拉坐標(biāo)系和拉格朗日坐標(biāo)系，既有優(yōu)點(diǎn)又有不足。歐拉方法相對(duì)簡(jiǎn)單，但是其不足在于：（a）對(duì)接觸間斷的分辨率不足；（b）在流體計(jì)算之前先要生成貼體坐標(biāo)。相反地，拉格朗日方法很好地分辨出接觸間斷（包括物質(zhì)介面和自由面），但它的缺點(diǎn)在于：（a）氣體動(dòng)力方程不能寫(xiě)成守恒型偏微分方程的形式，使得數(shù)值計(jì)算復(fù)雜和缺乏唯一性；（b）由于網(wǎng)格扭曲導(dǎo)致計(jì)算中斷。因此，計(jì)算流體力學(xué)的基本問(wèn)題除了深刻理解物理流動(dòng)之外，同時(shí)也要尋找"最優(yōu)的"坐標(biāo)系。統(tǒng)一坐標(biāo)系方法是《統(tǒng)一坐標(biāo)系下的計(jì)算流體力學(xué)方法》第一作者許為厚教授在前人坐標(biāo)變換的基礎(chǔ)上的進(jìn)一步發(fā)展，并在與其同事多年的合作中建立起來(lái)的。在計(jì)算流體力學(xué)的研究中尋找"最優(yōu)的"坐標(biāo)系肯定還會(huì)繼續(xù)下去，目前為止，統(tǒng)一坐標(biāo)系可較好地結(jié)合前兩種坐標(biāo)系的優(yōu)點(diǎn)，避免它們的不足。例如，統(tǒng)一坐標(biāo)系可以通過(guò)計(jì)算自動(dòng)生成網(wǎng)格，而且網(wǎng)格速度也可以考慮加入避免網(wǎng)格大變形的"擴(kuò)散"速度?！督y(tǒng)一坐標(biāo)系下的計(jì)算流體力學(xué)方法》首先回顧了一維和多維計(jì)算流體力學(xué)中的歐拉、拉格朗日以及ALE（Arbitrary-Lagrangian-Eulerian）方法的優(yōu)缺點(diǎn)以及各種移動(dòng)網(wǎng)格方法，然后系統(tǒng)介紹了統(tǒng)一坐標(biāo)法，用一些具體的算例闡明它和現(xiàn)有方法之間的關(guān)系。

書(shū)籍目錄

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

章節(jié)摘錄

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.

編輯推薦

《統(tǒng)一坐標(biāo)系下的計(jì)算流體力學(xué)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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