1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问,请联
系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
流体力学数学导引 Mathematical Intro to Fluid Mechanics
2.
授课院系
Originating Department
数学系 Mathematics
3.
课程编号
Course Code
MA328
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业选修课 Major Elective Courses
6.
授课学期
Semester
春季 Spring
7.
授课语言
Teaching Language
中英双语 English & Chinese
8.
他授课教师)
Instructor(s), Affiliation&
Contact
For team teaching, please list
all instructors
张振,数学系,副教授
慧园 3 417
zhangz@sustc.edu.cn
Zhang Zhen, Mathematics, Associate Professor
Room 417, Block 3, Wisdom Valley
zhangz@sustc.edu.cn
9.
/
方式
Tutor/TA(s), Contact
NA
10.
选课人数限额(不填)
Maximum Enrolment
Optional
授课方式
Delivery Method
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
OtherPlease specify
总学时
Total
11.
学时数
Credit Hours
48
2
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
数学分析 III 数学分析精讲
Mathematical Analysis III or Real Analysis
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
计算流体力学 Computational Fluid Dynamics
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
教授流体力学中的基本原理及其数学性质
Teach basic principles in Fluid Mechanics and their mathematical properties
16.
预达学习成果 Learning Outcomes
掌握 Navier-Stokes 方程和双曲方程的基本知识,为分析上和数值上的进一步研究奠定数学和物理基础
Master the fundamentals of Navier-Stokes equations and hyperbolic equations, provide mathematical and physical senses for the
future analytical and numerical study
17.
课程内容及教学日历 (如授课语言以英文为主,则课程内容介绍可以用英文;如团队教学或模块教学,教学日历须注明
主讲人)
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
3
第一部分:运动方程
Part I: The Equations of Motion
第一章:欧拉方程:守恒律,Reynolds 传输定理,热力学简介,不可压流和等熵流的欧拉方程,Bernoulli 定理(8 学时)
Chapter 1: Euler’s Equations: conservation laws, Reynolds transport theorem, introduction to thermodynamics, Euler equations for
incompressible and isentropic flows, Bernoulli’s theorem (8 hours)
第二章:旋度和涡:流场的涡度表示,Kelvin 回路定理,Helmholtz 定理,流函数-旋度分解(6 学时)
Chapter 2: Rotation and Vorticity: vorticity representation of flow fields, Kelvin’s circulation theorem, Helmholtz’s theorem,
streamfunction-vorticity formulation (6 hours)
第三章:Navier-Stokes 方程:应力张Cauthy 定理粘性Navier-Stokes 方程,边条件,无纲化Reynolds 数,润
滑模型,Helmoholtz-Hodge 分解,Stokes 方程,能量耗散,状态方程,声速,Mach 数(6 学时)
Chapter 3: Navier-Stokes Equations: stress tensor, Cauthy’s theorem, viscosity, Navier-Stokes equations, boundary conditions, non-
dimensionalization, Reynolds number, lubrication model, Helmoholtz-Hodge decomposition theorem, Stokes equations, energy
dissipation, equation of state, sound speed, Mach number (6 hours)
第二部分:有势流和微粘性流
Part II: Potential Flow and Slightly Viscous Flow
第四有势无旋流场数表Blasius Kutta-Joukowski d’Alembert’s 矛盾,有度,
势流,Green 函数(6 学时)
Chapter 4: Potential flow: irrotational flow, complex velocity and field, Blasius’ theorem, Kutta-Joukowski theorem, d’Alembert’s
paradox, potential vortex, almost potential flow, Green’s function (6 hours)
第五章:边界层:渐进展开,Prandtl 边界层方程,Navier-Stokes 方程近似解,边界层分离(5 学时)
Chapter 5: Boundary Layers: asymptotic expansions, Prandtl boundary layer equations, approximations to Navier-Stokes equations,
boundary layer separation (5 hours)
第六章:涡流层: Tchebysheff 不等式,大数定律,中心极限定理,随机游走和热方程,随机游走和涡流层,算法及其一致
性和收敛性,流映射(5 学时)
Chapter 6: Vortex sheets: Tchebysheff’s inequality, Law of large number, central limit theorem, random walk and heat equations,
random walk and vortex sheets, algorithm and its consistency and convergence, flow map (5 hours)
第七章:稳定性和分支:稳定不动点,Liapunov 稳定性定理,Hopf 分支定理(2 学时)
Chapter 7: Stability and Bifurcation: =Stable fixed points, Liapunov stability theorem, Hopf Bifurcation theorem (2 hours)
第三部分:其他专题
Part III: Other Topics
第八章:一维气体流:特征线,Riemann 不变量,稀疏波和激波,Riemann 问题(5 学时)
Chapter 8: Gas flow in one dimension: characteristics, Riemann invariants, rarefaction waves and shock waves, Riemann problems
(5 hours)
第九章:多相流:界面描述,Young-Laplace 方程,接触线和接触角,两相 Poiseuille 流(5 学时)
Chapter 9: Multiphase flows: interface description, Young-Laplace equation, contact line and contact angle, two-phase Poiseuille
flow (5 hours)
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18.
教材及其它参考资料 Textbook and Supplementary Readings
参考教材 Textbook
流体力学数学导论(英文版)A Mathematical Introduction to Fluid Mechanics, by A. J. Chorin, 世界图书出版公司北京公司,
2013.
流体力学(第 2 版)英文版 Fluid Mechanics, by L. D. Landau, 世界图书出版公司, 1999.
流体力学(上、下),吴望一 编著,北京大学出版社, 1982.
其他参考资料 Supplementary Readings
Navier-Stokes Equations: Theory and Numerical Analysis, by Roger Temam, North-Holland Publishing Company, 1977.
Fluid Mechanics, by Pijush K. Kundu, Ira M. Cohen, David R. Dowling, Academic Press, 2012.
An Introduction to Fluid Mechanics, by G. K. Batchelor, Cambridge University Press, 2000.
计算流体力学基础及其应用 Computational Fluid Dynamics, by 约翰 D. 安德森 John D. Anderson,吴颂平,刘赵森 , 机械工
业出版社, 2007.
课程评估 ASSESSMENT
19.
评估形式
Type of Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
课堂表现
Class Performance
小测验
Quiz
课程项目
Projects
平时作业
Assignments
30%
期中考试
Mid-Term Test
30%
期末考试
Final Exam
40%
期末报告
Final Presentation
其它(可根据需要改
写以上评估方式
Others (The above
may be modified as
necessary)
20.
记分方式 GRADING SYSTEM
A. 十三级等级制 Letter Grading
B. 二级记分制(通/不通过) Pass/Fail Grading
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课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/员会审议通过
This Course has been approved by the following person or committee of authority