Offered Every Spring


Credit Hours: 3-0-3
Prerequisites: CEE 6251 and ME 6601
Catalog Description: Numerical methods for solving the time-dependent Navier-Stokes equations in complex geometrics, including theory, implementation and applications. Crosslisted with CEE 7751.
Textbooks: Pieter Wesseling, Principles of Computational Fluid Dynamics; Springer-Verlag, 2000.
Joel H. Ferziger and Milovan Peric, Computational Methods of Fluid Dynamics, 3rd Edition, Springer-Verlag, 2001
Instructors: Marc K. Smith (ME), Fotis Sotiropoulos (CEE)
References:

C. Hirsch, Numerical Computation of Internal and External Flows, Vol. 1 and 2, John Wiley & Sons, Ltd., 1988.

G. F. Carey and Oden, J. T., Finite Elements: Fluid Mechanics, Vol. VI, Prentice-Hall, 1986.

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Mechanics, Springer-Verlag, 1988.
Goals:

This course gives the student experience with the numerical solution of viscous and inviscid fluid flows. The students will gain the following:

  • a knowledge of a variety of different numerical methods, their behavior, advantages, and disadvantages, and
  • the experience of solving a complex fluid flow problem numerically.
Topics:

  1. Introduction
  • A review of the Navier-Stokes equations and the surface-wave equations. Classification of PDEs.
  • The Finite-Difference Method
    • Derivation of basic differencing formulas, consistency, stability, and convergence of the method, and differencing schemes for the solution of hyperbolic, parabolic, and elliptic problems.
  • The Finite-Element Method
    • Derivation of the method; consistency, stability, and convergence; and applications.
  • The Finite-Volume Method
    • Derivation of the method; consistency, stability, and convergence; and applications.
  • Spectral Methods
    • Derivation of the method; consistency, stability, and convergence; and applications.
  • The Boundary-Element Method
    • Derivation of the method for potential and Stokes flows; consistency, stability, and convergence; and applications.