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:应力张量,Cauthy 定理,粘性,Navier-Stokes 方程,边界条件,无量纲化,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
第四章:有势流:无旋流,流场的复数表示,Blasius 定理,Kutta-Joukowski 定理,d’Alembert’s 矛盾,有势旋度,几乎有
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)