| 과목명 | 전산유체역학 기초 (Fundamentals of Computational Fluid Dynamics) | ||
|---|---|---|---|
| 교과목번호 | M2795.003500 | 학점 | 3 |
| 수업목표 | - 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. | ||
| 교재 및 참고문헌 | 1. Lecture Notes. | ||
| 평가방법 | 과제물(25%), 기말고사(45%), 프로젝트(25%), 출석 및 기타 (5%) | ||
| 강의계획 Chap 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. | |||
전산유체역학 기초
