計算流體動力學導論：有限體積法（第2版）（英文版） [An Introduction To Computational Fluid Dynamics:The Finite Volume Method Second Edition] pdf epub mobi txt 電子書 下載 2025

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[美] 費斯泰赫 著

圖書標籤:

• 計算流體動力學
• 有限體積法
• CFD
• 流體力學
• 數值方法
• 工程流體動力學
• 計算方法
• 第二版
• 高等教育
• 學術著作

齣版社： 世界圖書齣版公司

ISBN：9787510005572

版次：1

商品編碼：10104524

包裝：平裝

外文名稱：An Introduction To Computational Fluid Dynamics:The Finite Volume Method Second Edition

開本：16開

齣版時間：2010-04-01

用紙

內容簡介

　　We were pleasantly surprised by the ready acceptance of the first edition of our book by the CFD community and by the amount of positive feedback received over a period of 10 years. To us this has provided justification of our original plan， which was to provide an accessible introduction to this fast-growing topic to support teaching at senior undergraduate level， post- graduate research and new industrial users of commercial CFD codes. Our second edition seeks to enhance and update. The structure and didactic approach of the first edition have been retained without change， but aug- mented by a selection of the most important developments in CFD.

內頁插圖

目錄

Preface
Acknowledgements
1 Introduction
1.1 What is CFD?
1.2 How does a CFD code work?
1.3 Problem solving with CFD
1.4 Scope of this book

2 Conservation laws of fluid motion and boundary conditions
2.1 Governing equations of fluid flow and heat transfer
2.2 Equations of state
2.3 Navier-Stokes equations for a Newtonian fluid
2.4 Conservative form of the governing equations of fluid flow
2.5 Differential and integral forms of the general transport equations
2.6 Classification of physical behaviours
2.7 The role of characteristics in hyperbolic equations
2.8 Classification method for simple PDEs
2.9 Classification of fluid flow equations
2.10 Auxiliary conditions for viscous fluid flow equations
2.11 Problems in transonic and supersonic compressible flows
2.12 Summary

3 Turbulence and its modelling
3.1 What is turbulence?
3.2 Transition from laminar to turbulent }low
3.3 Descriptors of turbulent flow
3.4 Characteristics of simple turbulent flows
3.5 The effect of turbulent fluctuations on properties of the mean flow
3.6 Turbulent flow calculations
3.7 Reynolds-averaged Navier-Stokes equations and classical turbulence models
3.8 Large eddy simulation
3.9 Direct numerical simulation
3.10 Summary

4 The finite volume method for diffusion problems
4.1 Introduction
4.2 Finite volume method for one-dimensional steady state diffusion
4.3 Worked examples： one-dimensional steady state diffusion
4.4 Finite volume method for two-dimensional diffusion problems
4.5 Finite volume method for three-dimensional diffusion problems
4.6 Summary

5 The finite volume method for convection-diffusion problems
5.1 Introduction
5.2 Steady one-dimensional convection and diffusion
5.3 The central differencing scheme
5.4 Properties of discretisation schemes
5.5 Assessment of the central differencing scheme for convectiondiffusion problems
5.6 The upwind differencing scheme
5.7 The hybrid differencing scheme
5.8 The power-law scheme
5.9 Higher-order differencing schemes for convection-diffusion problems
5.10 TVD schemes
5.11 Summary

6 Solution algorithms for pressure-velocity
6.1 Introduction
6.2 The staggered grid
6.3 The momentum equations
6.4 The SIMPLE algorithm
6.5 Assembly ora complete method
6.6 The SIMPLER algorithm
6.7 The SIMPLEC algorithm
6.8 The PISO algorithm
6.9 General comments on SIMPLE， SIMPLER， SIMPLEC and PISO
6.10 Worked examples of the SIMPLE algorithm
6.11 Summary

7 Solution of discretised equations
7.1 Introduction
7.2 The TDMA
7.3 Application of the TDMA to two-dimensional problems
7.4 Application of the TDMA to three-dimensional problems
7.5 Examples
7.6 Point4terative methods
7.7 Multigrid techniques
7.8 Summary

8 the finite volume method for unsteady flows
8.1 Introduction
8.2 One-dimensional unsteady heat conduction
8.3 Illustrative examples
8.4 Implicit method for two- and three-dimensional problems
8.5 Discretisation of transient convection-diffusion equation
8.6 Worked example of transient convection-diffusion using QUICK differencing
8.7 Solution procedures for unsteady flow calculations
8.8 Steady state calculations using the pseudo-transient approach
8.9 A brief note on other transient schemes
8.10 Summary

9 Implementation of boomfary confftions
9.1 Introduction
9.2 Inlet boundary conditions
9.3 Outlet boundary conditions
9.4 Wall boundary conditions
9.5 The constant pressure boundary condition
9.6 Symmetry boundary condition
9.7 Periodic or cyclic boundary condition
9.8 Potential pitfalls and final remarks

10 Errors and uncertainty in CFD modelling
10.1 Errors and uncertainty in CFD
10.2 Numerical errors
10.3 Input uncertainty
10.4 Physical model uncertainty
10.5 Verification and validation
10，6 Guidelines for best practice in CFD
10.7 Reporting/documentation of CFD simulation inputs and results
10.8 Summary

11 Methods for dealing with complex geometries
11.1 Introduction
11.2 Body-fitted co.ordinate grids for complex geometries
11.3 Catesian vs. curvilinear grids - an example
11.4 Curvilinear grids - difficulties
11.5 Block-structured grids
11.6 Unstructured grids
11.7 Discretisation in unstructured grids
11.8 Discretisafion of the diffusion term
11.9 Discretisafion of the convective term
11.10 Treatment of source terms
11.11 Assembly of discretised equations
11.12 Example calculations with unstructured grids
11.13 Pressure-velocity coupling in unstructured meshes
11.14 Staggered vs. co-located grid arrangements
11.15 Extension of the face velocity interpolation method to unstructured meshes
11.16 Summary

12 CFD modelling of combustion
12.1 Introduction
12.2 Application of the first law of thermodynamics to a combustion system
12.3 Enthalpy of formation
12.4 Some important relationships and properties of gaseous mixtures
12.5 Stoichiometry
12.6 Equivalence ratio
12.7 Adiabatic flame temperature
12.8 Equilibrium and dissociation
12.9 Mechanisms of combustion and chemical kinetics
12.10 Overall reactions and intermediate reactions
12.11 Reaction rate
12.12 Detailed mechanisms
12.13 Reduced mechanisms
12.14 Governing equations for combusting flows
12.15 The simple chemical reacting system (SCRS)
12.16 Modelling of a laminar diffusion flame - an example
12.17 CFD calculation of turbulent non-premixed combustion
12.18 SCRS model for turbulent combustion
12.19 Probability density function approach
12.20 Beta pdf
12.21 The chemical equilibrium model
12.22 Eddy break-up model of combustion
12.23 Eddy dissipation concept
12.24 Laminar flamelet model
12.25 Generation oflaminar， flamelet libraries
12.26 Statistics of the non-equilibrium parameter
12.27 Pollutant formation in combustion
12.28 Modelling of thermal NO formation in combustion
12.29 Flamelet-based NO modelling
12.30 An example to illustrate laminar flamelet modelling and NO modelling of a turbulent flame
12.31 Other models for non-premixed combustion
12.32 Modelling ofpremixed combustion
12.33 Summary

13 Numedcal calculation of radiative heat transfer
13.1 Introduction
13.2 Governing equations of radiative heat transfer
13.3 Solution methods
13.4 Four popular radiation calculation techniques suitable for CFD
13.5 Illustrative examples
13.6 Calculation of radiative properties in gaseous mixtures
13.7 Summary

Appendix A Accuracy of a flow simulation
Appendix B Non-uniform grids
Appendix C Calculation of source terms
Appendix D Limiter functions used in Chapter 5
Appendix E Derivation of one-dimensional governing equations for steady， incompressible flow through a planar nozzle
Appendix F Alternative derivation for the term (n . grad Ai) in Chapter 11
Appendix G Some examples
Bibliography
Index

精彩書摘

　　The discussion of the k-e turbulence model, to which we return later, the material in Chapters 2 and 3 is largely self-contained. This allows the use of this book by those wishing tO concentrate principally on the numerical algorithms, but requiring an overview of the fluid dynamics and the math- ematics behind it for occasional reference in the same text.
　　The second part of the book is devoted to the numerical algorithms of the finite volume method and covers Chapters 4 to 9. Discretisation schemes and solution procedures for steady flows are discussed in Chapters 4 to 7. Chapter 4 describes the basic approach and derives the central difference scheme for diffusion phenomena. In Chapter 5 we emphasise the key prop- erties of discretisation schemes, conservativeness, boundedness and trans- portiveness, which are used as a basis for the further development of the upwind, hybrid, QUICK and TVD schemes for the discretisation of con- vective.terms. The non-linear nature of the underlying flow phenomena and the linkage between pressure and velocity in variable density fluid flows requires special treatment, which is the subject of Chapter 6. We introduce the SIMPLE algorithm and some of its more recent derivatives and also discuss the PISO algorithm. In Chapter 7 we describe algorithms for the solution of the systems of algebraic equations that appear after the discret- isation stage. We focus our attention on the well-known TDMA algorithm, which was the basis of early CFD codes, and point iterative methods with multigrid accelerators, which are the current solvers of choice.The theory behind all the numerical methods is developed around a set of worked examples which can be easily programmed on a PC. This pres- entation gives the opportunity for a detailed examination of all aspects of the discretisation schemes, which form the basic building blocks of practical CFD codes, including the characteristics of their solutions.
　　In Chapter 8 we assess the advantages and limitations of various schemes to deal with unsteady flows, and Chapter 9 completes the development of the numerical algorithms by considering the practical implementation of the most common boundary conditions in the finite volume method.
　　The book is primarily aimed to support those who have access to a CFD package, so that the issues raised in the text can be explored in greater depth. The solution procedures are nevertheless sufficiently well documented for the interested reader to be able to start developing a CFD code from scratch.
　　The third part of the book consists of a selection of topics relating to the application of the finite volume method to complex industrial problems. In Chapter 10 we review aspects of accuracy and uncertainty in CFD. It is not possible to predict the error in a CFD result from first principles, which creates some problems for the industrial user who wishes to evolve equip- ment design on the basis of insights gleaned from CFD. In order to address this issue a systematic process has been developed to assist in the quantifica- tion of the uncertainty of CFD output. We discuss methods, the concepts of verification and validation, and give a summary of rules for best practice that have been developed by the CFD community to assist users. In Chapter 11 we discuss techniques to cope with complex geometry. We review various approaches based on structured meshes: Cartesian co-ordinate systems, gen- eralised co-ordinate systems based on transformations, and block-structured grids, which enable design of specific meshes tailored to the needs of dif- ferent parts of geometry. We give details of the implementation of the finite volume method on unstructured meshes. These are not based on a grid of lines to define nodal.

前言/序言

　　We were pleasantly surprised by the ready acceptance of the first edition of our book by the CFD community and by the amount of positive feedback received over a period of 10 years. To us this has provided justification of our original plan， which was to provide an accessible introduction to this fast-growing topic to support teaching at senior undergraduate level， post- graduate research and new industrial users of commercial CFD codes. Our second edition seeks to enhance and update. The structure and didactic approach of the first edition have been retained without change， but aug- mented by a selection of the most important developments in CFD.
　　In our treatment of the physics of fluid flows we have added a summary of the basic ideas underpinning large-eddy simulation （LES） and direct numerical simulation （DNS）. These resource-intensive turbulence predic- tion techniques are likely to have a major impact in the medium term on CFD due to the increased availability of high-end computing capability.
　　Over the last decade a number of new discretisation techniques and solution approaches have come to the fore in commercial CFD codes. To reflect these developments we have included summaries of TVD techniques， which give stable， higher-order accurate solutions of convection-diffusion problems， and of iterative techniques and multi-grid accelerators that are now commonly used for the solution of systems of discretised equations. We have also added examples of the SIMPLE algorithm for pressure-velocity coupling to illustrate its workings.
　　At the rime of writing our first edition， CFD was firmly established in the aerospace， automotive and power generation sectors. Subsequently， it has spread throughout engineering industry. This has gone hand in hand with major improvements in the treatment of complex geometries. We have devoted a new chapter to describing key aspects of unstructured meshing techniques that have made this possible.
　　Application of CFD results in industrial research and design crucially hinges on confidence in its outcomes. We have included a new chapter on uncertainty in CFD results. Given the rapid growth in CFD applications it is difficult to cover， within the space of a single introductory volume， even a small part of the submodelling methodology that is now included in many general-purpose CFD codes. Our selection of advanced application material covers combustion and radiation algorithms， which reflects our local perspec- tive as mechanical engineers with interest in internal flow and combustion.

流體運動的計算之旅：一窺數值模擬的廣闊天地 本書旨在為讀者提供一個堅實的基礎，幫助他們理解和掌握現代流體力學研究與工程應用中至關重要的一環——計算流體力學 (CFD) 的核心原理與實踐方法。我們將聚焦於如何將復雜的流體物理現象，通過嚴謹的數學建模和高效的數值求解技術，轉化為計算機可以處理和分析的離散方程，從而揭示流體在各種工況下的行為模式。 我們深知，流體力學的領域博大精深，涵蓋瞭從宏觀的氣象預報到微觀的生物醫學流動。因此，本書的敘事結構被精心設計，力求在保持學術深度的同時，確保初學者也能平穩過渡，而有經驗的工程師也能從中汲取新的見解。本書的重點不在於對特定商業軟件的使用手冊進行詳述，而是著眼於方法論的構建與理解，這是構建任何成功流體模擬係統的基石。 第一部分：理論基石與物理背景 在正式進入數值方法之前，我們必須對流體運動背後的基本物理定律有一個清晰的認識。本部分將迴顧和闡述支配所有流體現象的基本控製方程組——納維-斯托剋斯（Navier-Stokes, N-S）方程。我們將深入探討這些方程的物理意義，分析其非綫性和耦閤特性，並討論在不同流動背景下（如不可壓縮、可壓縮、粘性、無粘性）方程的簡化形式及其適用範圍。理解這些微分方程的精髓，是後續將其轉化為可求解代數形式的前提。 我們還將詳細考察流體動力學的分類。從層流到湍流的過渡，是CFD領域最具挑戰性的課題之一。本書將對湍流的統計特性、雷諾平均納維-斯托剋斯（RANS）方程的引入進行必要的鋪墊，並簡要介紹大渦模擬（LES）和直接數值模擬（DNS）的基本思想，為讀者勾勒齣應對不同復雜度的工具箱。此外，邊界條件的選擇和處理，作為連接物理世界與數學模型的橋梁，其重要性不容忽視，我們將探討各種常見的入口、齣口、壁麵及自由邊界條件的物理設定與數學錶達。 第二部分：數值離散化的核心藝術 流體控製方程本質上是偏微分方程（PDEs），直接求解它們在解析上往往是睏難的，在工程實踐中更是幾乎不可能。因此，我們需要將空間和時間上的連續場域進行“數字化”處理，這就是數值離散化的藝術。 本部分是本書的核心內容之一。我們將係統地介紹幾種主要的離散化策略。首先，我們會從泰勒級數展開齣發，直觀地理解如何用離散點上的值來近似函數在某點的值，這是所有數值方法的齣發點。隨後，我們將把注意力轉嚮對 PDE 求解至關重要的方法： 1. 有限差分法（Finite Difference Method, FDM）的係統闡述： 雖然本書的側重點不在於此，但FDM是理解數值擴散、網格依賴性以及離散誤差的絕佳起點。我們將講解如何使用中心差分、迎風差分等不同格式來離散導數項，並討論這些選擇對解的穩定性和精度的深刻影響。 2. 有限體積法（Finite Volume Method, FVM）的深入剖析： 針對實際工程應用中對守恒性（如質量、動量、能量的守恒）的嚴格要求，FVM因其固有的守恒特性，成為瞭工業界的主流選擇。我們將詳細闡述控製方程如何在任意形狀的控製體積上通過積分形式被推導齣來。重點將放在通量計算上，即如何準確地評估穿過控製體積界麵（網格界麵）上的物理量輸運——這通常是決定解的準確性的關鍵步驟。 3. 網格生成與質量評估： 數值模擬的“場地”——計算網格——的質量直接決定瞭模擬的有效性。本部分將探討結構化網格、非結構化網格的生成技術，以及如何評估網格的質量指標（如正交性、光滑度），並討論網格無關性（Grid Independence）的驗證過程，確保我們的計算結果不是網格的産物，而是物理現象的真實反映。 第三部分：代數係統的求解與耦閤機製 完成離散化後，連續的 PDE 係統就被轉化為一個巨大的、通常是稀疏的非綫性代數方程組。如何有效地求解這些方程組，是決定計算效率和穩定性的關鍵。 1. 綫性係統的求解器： 我們將分類討論求解綫性代數方程組的方法。對於大型稀疏矩陣，迭代求解器（如雅可比法、高斯-賽德爾法，以及更高效的Krylov子空間方法，如GMRES或BiCGSTAB）的原理和收斂性分析是必不可少的。我們還會涉及預處理技術如何加速這些迭代過程。 2. 壓力-速度耦閤算法： 在不可壓縮流（或低速可壓縮流）中，N-S方程中壓力項與速度項的耦閤是一個主要的難點。本部分將詳細介紹解決這一問題的經典策略，特彆是SIMPLE（Semi-Implicit Method for Pressure Linked Equations）族算法及其後續發展，解釋這些算法如何通過壓力修正方程，在速度和壓力場之間建立反饋機製，確保解的一緻性。 3. 穩態與瞬態問題的處理： 求解策略會根據問題的性質有所不同。對於穩態問題，我們將討論如何利用鬆弛因子和亞迭代來穩定收斂過程。對於瞬態問題，我們將比較不同時間推進格式（如顯式、隱式、半隱式）的穩定性和精度特性，並探討如何選擇閤適的時間步長以平衡計算成本和時間分辨率。 第四部分：驗證、確認與高級主題概述 一個成功的模擬不僅需要順利運行，更需要證明其結果是可靠和有意義的。本部分將轉嚮計算結果的評估與應用。 1. 驗證（Verification）與確認（Validation）： 我們將區分這兩個至關重要的概念。驗證關注“我們是否正確地求解瞭方程？”（通常通過網格收斂性、時間步長收斂性測試和與解析解的對比來實現）。確認則關注“我們是否求解瞭正確的方程？”（即模型是否準確描述瞭真實的物理現象，需要與實驗或現場數據進行對比）。 2. 湍流模型的實際應用： 鑒於湍流的復雜性，我們不會迴避對實際工程中常用RANS湍流模型（如 $k-epsilon$ 模型、 $k-omega$ 模型及其剪應力輸運模型）的局限性與適用範圍的討論。理解這些模型的物理假設和數值實現上的睏難，是避免得齣誤導性結果的關鍵。 3. 高級議題的引介： 篇幅所限，我們無法對所有前沿技術進行詳盡展開，但會提供必要的概念介紹，包括動網格技術在模擬運動部件中的應用、多相流模型的挑戰，以及伴隨方法在優化設計中的潛力，引導讀者在掌握基礎後，繼續探索更廣闊的CFD前沿領域。 通過對這些理論、方法和實踐環節的係統梳理，本書緻力於培養讀者對計算流體動力學從物理概念到數值實現的全景式理解能力，使讀者能夠自信地構建、運行和解釋復雜的流體模擬項目。

評分☆☆☆☆☆

這本書的價值，對我而言，更多地體現在它為我打開瞭一扇通往CFD實際應用大門。作為一名希望將CFD技術應用於實際工程問題的工程師，我發現這本書提供瞭絕佳的橋梁。它並沒有迴避那些在實際工程中常見的挑戰，比如網格收斂性分析、數值穩定性問題、以及模型選擇的睏境。第二版在這些方麵的內容，比初版有瞭顯著的提升，尤其是在處理復雜邊界條件和真實世界流動的非綫性特性時，作者給齣的建議和方法論，極具指導意義。我特彆欣賞書中關於數值誤差的討論，以及如何通過閤理的設計來最小化這些誤差，這對於保證模擬結果的可靠性至關重要。英文原版在術語的使用上非常規範，這對於我在閱讀其他英文CFD文獻時，也起到瞭很好的鋪墊作用。總而言之，這本書不僅傳授瞭CFD的理論，更重要的是，它教會瞭我如何以一種係統和科學的方式去思考和解決CFD問題。

評分☆☆☆☆☆

對於我這樣一名剛踏入CFD研究領域的研究生來說，這本書簡直是一座金礦。初版我已經讀過，但第二版在許多細節上都做瞭精心的打磨和補充，讓我感覺耳目一新。作者對有限體積法的講解，從最基礎的守恒定律齣發，循序漸進地引入離散化、通量計算、壓力-速度耦閤等關鍵概念，整個過程非常流暢，邏輯性極強。我特彆喜歡書中對不同求解器和數值方法的對比分析，這有助於我理解它們各自的優缺點以及適用場景。例如，關於龍格-庫塔方法在時間積分中的應用，書中給齣的詳細推導和案例分析，讓我對如何選擇閤適的時間步長有瞭更清晰的認識。此外，第二版在湍流模型方麵的介紹也更加豐富，對RANS、LES等主流模型都進行瞭深入淺齣的講解，並且結閤瞭最新的研究進展。英文原版在學術錶達上非常嚴謹，這對於我們進行科研工作非常有益。這本書不僅僅是一本教材，更像是一位良師益友，指引我在這條充滿挑戰的研究道路上前行。

評分☆☆☆☆☆

這本書給我帶來的驚喜，遠不止於其內容的更新和擴充，更在於其教學方法的獨特魅力。我一直認為，學習CFD需要紮實的數學功底和清晰的物理直覺，而這本書恰恰在這兩方麵都做得非常齣色。作者在講解有限體積法時，並沒有僅僅停留在公式的羅列，而是花瞭大量篇幅去闡釋每一個數學步驟背後的物理意義。例如，在討論通量近似時，作者會詳細解釋為何需要進行插值，不同的插值方法會對計算結果産生怎樣的影響，這讓我對CFD的離散化過程有瞭更深刻的理解。第二版在處理非結構網格方麵的介紹，也比初版更加細緻，這對於解決復雜幾何形狀的流動問題至關重要。而且，書中提供的許多例題，都具有很強的代錶性，涵蓋瞭從簡單的不可壓縮流動到更復雜的傳熱傳質問題，讓我能夠通過實踐來鞏固理論知識。英文原版的語言風格非常專業，但不失親切感，即使是復雜的概念，也能被清晰地錶達齣來。

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這本書簡直是一場知識的盛宴，特彆是對於那些像我一樣，渴望深入理解計算流體動力學（CFD）精髓的讀者來說。初版我就相當喜愛，這次的第二版更是讓我驚喜連連。作者在保持原有清晰邏輯和紮實理論框架的基礎上，對內容進行瞭顯著的擴充和更新，這一點在實操層麵給我帶來瞭巨大的便利。舉例來說，書中對於有限體積法（FVM）各個方麵的講解，從最基礎的離散化概念，到高級的通量求解器和湍流模型，都進行瞭詳盡的闡述。我尤其欣賞作者對於數學推導的細緻呈現，每一步都力求嚴謹，不會讓讀者在理解上産生斷層。而且，書中穿插的那些“為什麼”的解釋，比如為什麼選擇某種格式，為什麼需要特定的邊界條件，這些都是我曾經在自學過程中感到睏惑的地方，現在都得到瞭令人滿意的解答。英文版更是原汁原味，語言的精準性保證瞭技術的傳達不失毫厘。讀這本書就像是跟隨一位經驗豐富的嚮導，一步步探索CFD的奇妙世界，你會感覺自己不再是被動接受信息，而是真正地掌握瞭這門強大的工具。

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作為一個在工程領域摸爬滾打瞭多年的從業者，我一直在尋找一本能夠係統性地梳理CFD理論，同時又能指導實際應用的權威著作。這本書，尤其是第二版，可以說完美地填補瞭我一直以來的需求空白。它不是那種隻停留在理論層麵，對實際問題避而不談的教科書，也不是那種缺乏理論支撐，隻有代碼和案例的實用手冊。作者巧妙地將理論與實踐融為一體，通過大量的例子和圖示，將抽象的數學概念形象化，讓我能夠清晰地看到有限體積法是如何一步步從數學模型轉化為計算機可以執行的模擬過程。第二版在數值算法的介紹上，感覺比初版更加深入和全麵，特彆是關於高階精度格式和一些現代化的數值技術，這對於我進行更精確、更高效的CFD模擬至關重要。這本書的英文錶達非常專業且易於理解，即使遇到一些復雜的術語，作者的解釋也足夠到位，不會讓人望而卻步。我強烈推薦這本書給所有希望在CFD領域打下堅實基礎，並能夠將其應用於解決實際工程問題的讀者。

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經典書籍，學習流體力學很好的入門

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這本導論書質量非常好，性價比很高，下次還會買，物流真的非常快。

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