ACFD1

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Course Outline
Course No.

M2795.005500

Lecture No.   Course Title

Advanced Computational Fluid Dynamics I

(Basic Elements and Scalar Conservation Laws)
Credits 3
Instructor Name : Chongam Kim Homepage : http://mana.snu.ac.kr
E-mail : chongam@snu.ac.kr office : 880-1915
1. Goals

This course will deal with understanding basic mathematical and physical nature of PDEs and studying various numerical techniques to discretize the equations. We will also study fundamental numerical concepts such as consistency, stability and convergence, and apply concepts to analyze each scheme's numerical behavior.

2. Textbook
& References

1. Lecture note

2. Computational fluid mechanics and heat transfer by Tannehill, Anderson and Pletcher, 2nd Ed., Taylor & Francis

3. Finite volume methods for hyperbolic problems by Leveque, Cambridge

4. Riemann Solvers and Numerical Methods for Fluid Dynamics by Toro, Springer

3. Evaluation

Homework(30%), Final exam (35%), Term project(35%)

4. Lecture Plan Week Contents
1

Classification of 2nd order PDE

2

Basic discretization techniques, numerical dissipation and dispersion

3

Stability and CFL condition, Linear stability analysis

4

Model equations I - parabolic PDE: basic implicit and explicit schemes

5

ADI, AF-ADI schemes

6

Model equations II - Elliptic PDE: iterative methods, basic convergence acceleration techniques

7 Model equations III - Hyperbolic PDE: basic theory of scalar conservation law
8

Central differencing, semi-discrete methods with R-K time stepping

9

Nonlinear stability and hyperbolic PDE, monotonicity and Godunov’s theorem

10

TVD schemes for linear and nonlinear SCL, ENO interpolation

11

Introduction to higher-order methods

12

Basic discretization methods of the 1-D Euler equations

13

Flux vector splitting and Flux difference splitting

14

Riemann solvers & Term project

15

Final Exam.