## ACFD1

Course No. |
M2795.005500 |
Lecture No. | Course Title |
Advanced Computational Fluid Dynamics I (Basic Elements and Scalar Conservation Laws) |
Credits | 3 | ||
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Instructor | Name : Chongam Kim | Homepage : http://mana.snu.ac.kr |
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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. |
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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 |
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3. Evaluation |
Homework(30%), Final exam (35%), Term project(35%) |
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4. Lecture Plan | Week | Contents | ||||||

1 |
Classification of 2nd order PDE |
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2 |
Basic discretization techniques, numerical dissipation and dispersion |
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3 |
Stability and CFL condition, Linear stability analysis |
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4 |
Model equations I - parabolic PDE: basic implicit and explicit schemes |
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5 |
ADI, AF-ADI schemes |
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6 |
Model equations II - Elliptic PDE: iterative methods, basic convergence acceleration techniques |
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7 | Model equations III - Hyperbolic PDE: basic theory of scalar conservation law | |||||||

8 |
Central differencing, semi-discrete methods with R-K time stepping |
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9 |
Nonlinear stability and hyperbolic PDE, monotonicity and Godunov’s theorem |
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10 |
TVD schemes for linear and nonlinear SCL, ENO interpolation |
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11 |
Introduction to higher-order methods |
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12 |
Basic discretization methods of the 1-D Euler equations |
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13 |
Flux vector splitting and Flux difference splitting |
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14 |
Riemann solvers & Term project |
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15 |
Final Exam. |