전산유체역학 기초

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강의소개
교과목번호 M2795.003500 강좌번호   과목명 전산유체역학 기초(Fundamentals of Computational Fluid Dynamics) 학점 3
담당교수 성명 : 김종암 홈페이지 : http://mana.snu.ac.kr
E-mail : chongam@snu.ac.kr office : 02-880-1915
1.수업목표 본 강의는 대학원 과정의 고급전산유체역학을 위한 기초입문과정으로서 공기역학, 압축성유체역학 등에서 학습하였던 유동의 지배 방정식 또는 이완 관련된 (편)미분 방정식을 이산화 하여 수치해석을 수행하는 과정과 함께 이와 관련된 기본적인 개념들을 다룬다. 주로 유한체적법에 기초한 다양한 수치기법들을 기반으로 1차원, 2차원 유동을 계산하는 수치해석코드를 만들어 보고, 실제적인 유동문제 해석에 적용하여 그 장단점을 분석해본다. 아울러 EDISON_CFD를 활용한 계산실습도 병행해서 수행한다.
2.교재 및
참고문헌

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.평가방법 출석 및 과제물(10%), 중간고사(35%), 기말고사(40%), 프로젝트(15%)
4.강의계획 강의내용
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