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MAE 560 601 Computational Fluid Mechanics

MAE 560 601 Computational Fluid Mechanics

July 5, 2023

3 Credit Hours

Chi-An Yeh

Asst Professor

Prerequisite

MA 501 Advanced Engineering Thermodynamics or MA 512, MAE 550 Foundations Of Fluid Dynamics 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

  • Governing equations for fluid flow and their different forms
  • Mathematical classification of partial differential equations: hyperbolic, parabolic, and elliptic
  • Numerical interpolation and differentiation: finite-difference approximations
  • Time integration methods
  • Numerical convergence, compatibility, and stability
  • Solutions of wave and heat equations
  • Linear systems of equations
  • Solutions of Laplace and Poisson equations
  • Staggered grid and fractional step method for the incompressible Navier–Stokes Equations
  • Solutions of the incompressible Navier–Stokes Equations
  • (Time permitting) Finite-volume and spectral methods
  • (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