Fundamentals of Computational Fluid Dynamics

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Course Outline
Course No. M2795.003500 Lecture No.   Course Title Fundamentals of Computational Fluid Dynamics 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 provides fundamental numercial studies on computational approaches for partial differential equations associated with compressible flow physics which have been studied in undergraduate courses, such as aerodynamics, compressible fluid dynamics, (applied) fluid mechanics, etc. Students are encouraged to write one-dimensional and/or two-dimensional numerical simulation codes, by applying the numerical methods studied in this course, to calculate actual flow fields. At the same time, computational practices based on EDISON_CFD flatform will be carried out in parallel.

2. Textbook
& References

1. Lecture note

2. Computational Fluid Dynamics : Volume 1, 4th Edition-Klaus A. Hoffmann, Steve T. Chiang-Engineering Education System-2000

3. Computational Fluid Mechanics and Heat Transfer, 3rd Edition-Richard H. Pletcher, John C. Tannehill, Dale Anderson-CRC Press-2011

3. Evaluation Attendance & Homework(10%), Midterm(35%), Final exam(40%), Term project(15%)
4. Lecture Plan Week Contents
1

Chapter 1. Classification of Partial Differential Equations
 - Second-order linear PDE, Elliptic PDE, Parabolic PDE, Hyperbolic PDE

2 Chapter 1. Classification of Partial Differential Equations
 - Systems of equations, Initial and boundary conditions
3 Chapter 2. Basic Discretizations and Linear Stability
 - Basic discretization options, Finite difference approximations, Basic temporal discretizations
4 Chapter 2. Basic Discretizations and Linear Stability
 - Basic discretization options, Finite difference approximations, Basic temporal discretizations
5 Chapter 2. Basic Discretizations and Linear Stability
 - Linear stability analysis, CFL condition, Lax’s equivalence theorem
6 Chapter 3. Model Equation I : Heat Equation (Parabolic PDE)
 - Basic implicit and explicit schemes, DuFort-Frankel scheme, Stability analysis
7

Chapter 3. Model Equation I : Heat Equation (Parabolic PDE)
 - Multi-dimensional cases, Basic discretization, Fractional step method, ADI, AF-ADI

8

Chapter 4. Model Equation II : Laplace Equation (Elliptic PDE)
 - Basic discretization, Matrix inverse problem, Direct method, Tri-diagonal matrix inverse algorithm

9 Chapter 4. Model Equation II : Laplace Equation (Elliptic PDE)
 - Iteration(relaxation) method, Convergence analysis, Stability analysis, Jacobi method, Gauss-Seidel method
10 Chapter 4. Model Equation II : Laplace Equation (Elliptic PDE)
 - Over-relaxation method, Stability analysis, Multigrid method
11

Chapter 5. Model Equation Ⅲ : Advection Equation (Hyperbolic PDE)
 - Definition of hyperbolic PDE, Basic theory of scalar conservation law, Finite volume discretization

12

Chapter 5. Model Equation Ⅲ : Advection Equation (Hyperbolic PDE)
 - Numerical schemes for hyperbolic PDE (Lax-Friedrich scheme, Upwind method for advection, Lax-Wendroff scheme)

13 Chapter 5. Model Equation Ⅲ : Advection Equation (Hyperbolic PDE)
 - Numerical schemes for hyperbolic PDE (MacCormack scheme, Beam-Warming scheme, Crank-Nicolson scheme), Multi-step method & Multi-stage Runge-Kutta method
14 Chapter 6. Non-linear Stability & Hyperbolic PDE
 - Non-linear scheme, Gibbs phenomenon, Godunov’s barrier theorem on monotonicity, Total variation concept
15

EDISON Programming for Term Project