MAE 560 601 Computational Fluid Mechanics

3 Credit Hours

Prerequisite

MA 501 or MA 512, MAE 550 or MAE 557 (co-req)

Course Objectives

Practice the fundamental theories behind numerical solutions to partial differential equations. Write computer programs from scratch to solve partial differential equations including wave equation, heat equation, Laplace/Poisson equation, and the incompressible Navier-Stokes equations.

Course Outline

1. Governing equations for fluid flow and their different forms
2. Mathematical classification of partial differential equations: hyperbolic, parabolic, and elliptic
3. Numerical interpolation and differentiation: finite-difference approximations
4. Time integration methods
5. Numerical convergence, compatibility, and stability
6. Solutions of wave and heat equations
7. Linear systems of equations
8. Solutions of Laplace and Poisson equations
9. Staggered grid and fractional step method for the incompressible Navier–Stokes Equations
10. Solutions of the incompressible Navier–Stokes Equations
11. (Time permitting) Finite-volume and spectral methods
12. (Time permitting) Data-based modal analysis

Textbooks

None, but a list of references and optional texts will be provided.

Software Requirements

For in-class demonstrations we will simply use MATLAB, but for homework and projects you are free to use any other languages of your own preference (C/C++, Fortran, Python, Julia, etc).

Updated 6/23/2023