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ME 7751: Computational Fluid Mechanics
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.
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| Topics: |
- 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.
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