Explore the fundamentals of Computational Fluid Dynamics (CFD) in this comprehensive 32-hour course. Delve into topics such as computer representation of arrays and functions, finite differences, Laplace equation, linear wave equation, and one-dimensional Euler equations. Learn about stability analysis, boundary conditions, and advanced techniques like flux vector splitting and Roe's averaging. Discover methods for accelerating convergence, including preconditioning, dual time stepping, and multigrid methods. Gain insights into parallel computing and the calculus of variations. Through lectures and demonstrations, develop a strong foundation in CFD principles and their practical applications in solving complex fluid dynamics problems.
Overview
Syllabus
Mod-01 Lec-01 Introduction, Why and how we need computers.
Mod-01 Lec-02 Representing Arrays and functions on computers.
Mod-01 Lec-03 Representing functions - Box functions.
Mod-01 Lec-04 Representing functions - Polynomials & Hat functions.
Mod-01 Lec-05 Hat functions, Quadratic & Cubic representations.
Mod-01 Lec-06 Demo - Hat functions, Aliasing.
Mod-01 Lec-07 Representing Derivatives - finite differences.
Mod-01 Lec-08 Finite differences, Laplace equation.
Mod-01 Lec-09 Laplace equation - Jacobi iterations.
Mod-01 Lec-10 Laplace equation - Iteration matrices.
Mod-01 Lec-11 Laplace equation - convergence rate.
Mod-01 Lec-12 Laplace equation - convergence rate Continued.
Mod-01 Lec-13 Demo - representation error, Laplace equation.
Mod-01 Lec-14 Demo - Laplace equation, SOR.
Mod-01 Lec-15 Laplace equation - final, Linear Wave equation.
Mod-01 Lec-16 Linear wave equation - Closed form & numerical solution, stability analysis.
Mod-01 Lec-17 Generating a stable scheme & Boundary conditions.
Mod-01 Lec-18 Modified equation.
Mod-01 Lec-19 Effect of higher derivative terms on Wave equation.
Mod-01 Lec-20 Artificial dissipation, upwinding, generating schemes.
Mod-01 Lec-21 Demo - Modified equation, Wave equation.
Mod-01 Lec-22 Demo - Wave equation / Heat Equation.
Mod-01 Lec-23 Quasi-linear One-Dimensional. wave equation.
Mod-01 Lec-24 Shock speed, stability analysis, Derive Governing equations.
Mod-01 Lec-25 One-Dimensional Euler equations - Attempts to decouple.
Mod-01 Lec-26 Derive Eigenvectors, Writing Programs.
Mod-01 Lec-27 Applying Boundary conditions.
Mod-01 Lec-28 Implicit Boundary conditions.
Mod-01 Lec-29 Flux Vector Splitting, setup Roe’s averaging.
Mod-01 Lec-30 Roe’s averaging.
Mod-01 Lec-31 Demo - One Dimensional flow.
Mod-01 Lec-32 Accelerating convergence - Preconditioning, dual time stepping.
Mod-01 Lec-33 Accelerating convergence, Intro to Multigrid method.
Mod-01 Lec-34 Multigrid method.
Mod-01 Lec-35 Multigrid method - final, Parallel Computing.
Mod-01 Lec-36 Calculus of Variations - Three Lemmas and a Theorem.
Mod-01 Lec-37 Calculus of Variations - Application to Laplace Equation.
Mod-01 Lec-38 Calculus of Variations -final & Random Walk.
Mod-01 Lec-39 Overview and Recap of the course.
Taught by
aerospace engineering
