# AAE 41200 Introduction to Computational Fluid Dynamics

Description:

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

Offered: Fall

Pre-requisite: AAE 334 or equivalent

Co-requisite: None

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.

## Course Objective:

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.

Necessary Background:

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