# 전산유체역학 기초

강의소개
과목명 교과목번호 전산유체역학 기초 (Fundamentals of Computational Fluid Dynamics) M2795.003500 3 - 유체현상과 관련된 물리적/수학적 지식을 바탕으로 고급전산유체역학 지식을 습득하기 위한 기초적   입문과정 학습.- 유동의 지배방정식과 연관된 간단한 편미분 방정식의 기본적인 이산화(discretization) 과정을 배우고   유한차분법(Finite Difference Method, FDM) 및 유한체적법(Finite Volume Method, FVM)과 관련된  기본개념 이해.- 유한차분법 및 유한체적법에 기반한 기초적 수치기법을 배우고 이를 바탕으로 1차원 및 2차원 모델방정식을   계산하는 코딩 연습 및 계산결과 분석.- EDISON_CFD를 통한 계산실습 및 term project 수행. 1. Lecture Notes.2. Computational Fluid Mechanics and Heat Transfer   by Pletcher, Tannehill and Anderson, CRC Press.3. Computational Fluid Dynamics, Vol. 1   by Hoffmann and Chiang, Engineering Education System.4. 온라인 강의 '전산유체역학(Computational Fluid Dynamics, CFD) 이론 및 실습'  Available from (https://mooc.edison.re.kr/cfd/intro.html) 과제물(25%), 기말고사(45%), 프로젝트(25%), 출석 및 기타 (5%) 강의계획Chap 1. Introduction and Classification of Partial Differential Equations.  - Brief introduction of computational fluid dynamics. - Second-order linear PDE, Elliptic PDE, Parabolic PDE, Hyperbolic PDE. - Systems of equations, initial and boundary conditions. Chap 2 : Basic Discretization and Linear Stability.- Basic discretization options, Finite difference approximation, Basic temporal discretization.- Concept of stability, Modified equation, Numerical dissipation and numerical dispersion.- Linear stability analysis and Von Neumann stability, CFL condition, Relationship among consistency,  stability and convergence. Chap 3: Model Equation of Parabolic PDE : Heat Equation.- Basic implicit and explicit schemes, Stability analysis.- Multi-dimensional cases, Basic discretization, Fractional step method, ADI scheme and AF-ADI scheme. Chap 4: Model Equation of Elliptic PDE: Laplace Equation.- Basic discretization, Matrix inverse problem, Direct method, Inversion of tri-diagonal matrix.- Iteration(relaxation) method, Basic convergence and stability analysis, Jacobi method,   Gauss-Seidel method.- Over-relaxation method, Multigrid method. Chap 5: Model Equation of Hyperbolic PDE: Advection Equation.- Definition of hyperbolic PDE, Basic theory of scalar conservation law, Finite volume discretization   and conservative scheme.- Basic numerical schemes for hyperbolic PDE (Lax-Friedrich scheme, Upwind method,   Lax-Wendroff scheme, MacCormack scheme, Beam-Warming scheme, Crank-Nicolson scheme).- Time-integration method (Multi-step method, Multi-stage Runge-Kutta method)- Gibbs phenomenon, Godunov's barrier theorem on monotonicity, Non-linear scheme   and concept of total variation (optional). Review & Q/A. EDISON_CFD Practices, Term Project and Final Exam.