AAE 51200: Computational Aerodynamics
Finite difference methods for solving fluid flow problems. Review of classification of partial differential equations, well-posed problems, and discrete approximation of partial differential equations. Matrix and von Neumann stability analysis. Consistency and convergence. Grid generation: elliptic, hyperbolic, and transfinite mesh generation methods. Methods for solving the unsteady Euler equations: finite-volume formulations, flux-split and flux-difference formulations, shock-capturing, formulation of boundary conditions, artificial viscosity models, and multi-grid acceleration.
Format: 3 hrs lecture per week
Credit hours: 3
Status: Elective, Aerodynamics
Pre-requisite: AAE 412 or ME581
Course Instructor: Prof. Williams
Text: C. Hirsch Numerical Computation of Internal and External Flows Vol 2, Computational Methods for Inviscid and Viscous Flows Wiley, 1990 (recommended)
Assessment Method: Students will be graded based on a sequence of 8-10 written projects.
Students learn how to formulate and solve discrete models of fluid flow problems for incompressible and compressible, inviscid and viscous fluids. They will be able to assess the accuracy of numerical solutions by comparison to known solutions of simple test problems and by mesh refinement studies. They will be able to select appropriate algorithms for different kinds of problems.
It is expected that you will have had some background in numerical methods, for example through AAE412, ME581, or equivalents. You should be conversant with some suitable programming language, like Fortran or C. Many problems can also be done in MATLAB, particularly the smaller problems. I will use Matlab for classroom demonstrations, so familiarity with that language is important.
Topics (number of Lectures):
1) (1 week) Field Representations, Grids, Interpolation
2) (1 week) Euler Equations (Conservation Laws)
3) (1 week) Linearized Euler: characteristics,First Order Wave equations
4) (2 weeks) numerical solutions of linear 1st order wave equations
5) (1 week) Quasi-1D nonlinear flows
6) (4 weeks) 2D and axisymmetric flows
7) (2 weeks) Extensions to viscous and other effects.
8) (2weeks) Steady state convergence acceleration techniques
Relationship of course to program objectives:
The course is primarily intended for graduate students and advanced undergraduates interested in aerodynamics and propulsion (PO 1). Students learn 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 H. Williams
Date: March 12, 2001