本教学案例设计坚持“紧跟学科发展、突出能力提高”，面向能源、航天航空、化工等领域国家重大需求，科教相长，及时更新研究生课程案例教学内容，将流动传热问题数值仿真教学案例设计与国家重大需求高度匹配，设计了包含流动传热数值模拟自编程基础案例以及面向芯片热管理、电池热管理、太阳能高效利用等为背景的能力提高实践案例。通过上述多层次的案例，既夯实研究生基础理论知识，又培养研究生运用数值方法解决实际工程问题的能力，达到培养研究生的创新意识和创新能力的目的

2.1 Grid Generation (网格生成)（Domain Discretization） 2.2 Taylor Expansion and Polynomial Fitting (多项式拟合)for Equation Discretization 2.3 Control Volume （控制容积）and Heat Balance Methods for Equation Discretization

4.1 Two ways of discretization of convection term 4.2 CD and UD of the convection term 4.3 Hybrid and power-law schemes 4.4 Characteristics of five three-point schemes

4.5 Discussion on false diffusion 4.6 Methods for overcoming or alleviating effects of false diffusion 4.7 Discretization of multi-dimensional problem and B.C. treatment

3.1 1-D Heat Conduction Equation 3.2 Fully Implicit Scheme of Multi-dimensional Heat Conduction Equation 3.3 Treatments of Source Term and B.C

3.4 TDMA & ADI Methods for Solving ABEs 3.6 Fully Developed HT in Rectangle Ducts 3.5 Fully Developed HT in Circular Tubes

《数值传热学》课程教学大纲 Numerical Heat Transfer（硕士）

7.3 Conservation of Discretized Equations 7.4 Transportive Property of Discretized 7.5 Sign-preservation Principle for Analyzing 7.3.1 Definition and analyzing model 7.3.2 Direct summation method 7.3.3 Conditions for guaranteeing conservation 7.3.4 Discussion－expected but not necessary 7.3.2 Direct summation method (直接求和法) 7.3.4 Discussion－Conservation is expected but not 7.4.1 Essential (基本的) difference between 7.4 Transportive (迁移)Character of Discretized 7.4.2 CD of diffusion term can propagate(传播) 7.4.3 Analysis of transport character of 7.4.4 Upwind scheme of convection term 7.4.5 Discussion on transport character of 7.4.1 Essential difference between convection 7.4 Transportive Property of Discretized Equations 7.4.3 Analysis of transport character (迁移特性) of 7.4.4 Upwind scheme (迎风格式) of convective 7.4.5 Discussion on transportive character of 7.5 Stability analysis of discretized diffusion￾convection equation

8.1 Introduction to turbulence 8.2 Time-averaged governing equation for incompressible convective heat transfer 8.3 Zero-equation and one-equation model 8.4 Two-equation model 8.5 Wall function method 8.6 Low-Reynolds number k-epsilon model 8.7 Brief introduction to recent developments

7.1 Consistence, Convergence and Stability of Discretized Equations 7.1.1 Truncation error and consistence(相容性） 7.1.3 Round off error （舍入误差）and stability （稳定性） of initial problems（初值问题） 7.1.4 Examples 7.1.2 Discretization error（离散误差） and convergence(收敛性） 7.2 von Neumann Method for Analyzing Stability of Initial Problems 7.2.1 Propagation of error vector with time 7.2.2 Discrete Fourier expansion 7.2.3 Basic idea of von Neumann analysis 7.2.4 Examples of von Neumann analysis 7.2.5 Discussion on von Neumann analysis