AAE 41200 Introduction to Computational Fluid Dynamics
Introductory course in the formulation and application of finite difference methods for solving fluid flow problems. Classification of partial differential equations and formulation of well-posed problems. Discrete approximation of partial differential equations: stability, consistency, and convergence. Finite-volume formulations. Survey of methods for solving hyperbolic, elliptic, and parabolic problems. Formulation of discrete boundary conditions. Application of methods to one- and two-dimensional flow problems.
Format: 3 hrs lecture per week
Credit hours: 3
Status: Aerodynamics or Propulsion Elective
Pre-requisite: AAE 334 or equivalent
Course Instructor: Professor Blaisdell
Text: None; handouts and references are used
Assessment Method: Grades are based on a series of written projects, typically 8-10 depending on complexity.
Students are expected to learn the basics of finite difference approximations of Partial Differential Equations, including error estimation, on logically rectangular grids. They should be able to assess the accuracy of a numerical solutions by comparison to known solutions of simple test problems and by mesh refinement studies. Students should learn how CFD is used to predict forces on airfoils.
Students must have had basic fluid mechanics (eg. AAE333), including the incompressible Navier-Stokes equations, and potential flow. Ability to write basic Matlab code is essential.
Topics (number of Lectures):
1) (3 lec) Introduction and outline
2) (6 lec.) Finite Difference Approximations of derivatives and D.E.s in 1D
Project 1: Solving Linear ODE boundary value problems
3) ( 6 lec.) Nonlinear BVPs, Newtons Method
Project 2: Steady state heat conduction in an annulus with temperature dependent conductivity
4) (6 lec) Visualization of 2D fields: grid construction, generalized coordinates,CONTOUR, MESH, SURF, PLOT3, QUIVER
Project 3: Visualization of specified 2D scalar and vector fields
5) (6 lec) Finite Difference approximations of partial derivatives and PDE's
Project 4: Incompressible potential flow in an expansion.
Project 5: Computing derivatives of specified fields
6) (6 lec) Inflow/Outflow boundary conditions; external flow
Project 6: Incompressible Irrotational Flow over a Joukowski Airfoil by FDM
7) (6 lec) Convection Problems: Stability issues
Project 7: Passive convection of a tracer in a specified flow field.
8) (6 lec) Convection/Diffusion Problems
Project 8: Navier-Stokes solutions for flow over a circular cylinder
Project 9: Navier-Stokes solution for flow over an airfoil.
Relationship of course to program objectives:
The course is primarily of use to students interested in aerodynamics and propulsion (PO 1) Students learn about how to formulate and solve computational problems arising in the flow of fluids (PO 2a). Students are expected to communicate their work graphically and in writing (PO 2c). Teamwork and oral communications (PO 2b,c) are sometimes emphasized, depending on enrollment.
Prepared by: Marc Williams
Date: February 13, 2001