## AEM 5251: Computational Fluid Mechanics

### Catalog Description

**Syllabus**

**AEM 5251**

Computational Fluid Mechanics

3 Credits

**Catalog Description: **

Emphasis on introductory concepts in finite difference and finite volume methods as applied to various ordinary and partial differential model equations in fluid mechanics; fundamentals of spatial discretization and numerical integration; numerical linear algebra. Introduction to engineering and scientific computing environment. Advanced topics may include finite element methods, spectral methods, grid generation, turbulence modeling.

**Course Web Address:**

http://www.aem.umn.edu/courses/aem5251/

**Prerequisites by Topic: **

- Fluid Mechanics (AEM 4201)
- Programming: (CSCI 1113 or equiv.)

**Text: **

Zikanov, *Essential
Computational Fluid Dynamics*, Wiley, 9780470423295

**Format of Course:**

3 lecture hours per week

**Computer Usage:**

Computer programming required in homework assignments and term project.

**Course Objectives: **

Develop an understanding of introductory concepts in computational fluid mechanics with emphasis on the numerical solution of ordinary and partial differential equations; solution of ODEs by numerical integration; finite difference and finite volume methods for parabolic, elliptic, and hyperbolic PDEs (techniques for single and multi-dimensional problems); numerical linear algebra. Ability to implement and utilize various numerical methods and basic mathematical analysis for canonical problems in fluid mechanics. Develop advanced skills in Matlab and programming languages such as C/C++ & Fortran.

**Course Outcomes:**

Students will demonstrate the following in homework, tests, and the term project:

- An ability to identify, formulate, and solve engineering problems by approximating complex physical systems in fluid flow by simplified canonical models.
- A knowledge of fluid mechanics and its mathematical description.
- An ability to apply knowledge of math and science to engineering by describing a continuous fluid-flow phenomena in a discrete numerical sense.
- An ability to use the techniques, skills, & engineering tools necessary for engineering practice by applying numerical methods to a "real-world" fluid-flow problem, integrating various numerical techniques in formulating a numerical solution method for that problem, and using computational tools such as Matlab and programming languages (Fortran, C/C++).
- An ability to analyze and interpret data obtained from the numerical solution of fluid flow problems.
- An ability to communicate effectively by writing the term project in a structured technical report format and by learning how to ask questions in class.

**Relationship of course to
program objectives:**

This course develops students’ knowledge of fluid mechanics and aerodynamics, as well as improving their problem solving abilities. Additionally, the term project improves students’ written communication and computer skills.

**Relationship of course to
program outcomes:**

This course provides the following outcomes:

- Apply mathematics
- Identify engineering problems
- Lifelong learning
- Engineering tools
- Aerodynamics

**Course Outline:**

** **

Lecture |
Topic |

6 |
Introduction and Review |

6 |
Numerical Solution of ODEs |

6 |
Methods for Parabolic Equations |

6 |
Methods for Elliptic Equations |

6 |
Methods for Hyperbolic Equations |

6 |
Systems of Equations |

6 |
Advanced Topics |

**Outcome Measurement:**

Homework, tests and a project.

**Student Survey Questions:**

** **

This course improved my ability to do the following:

- Apply knowledge of math, science, and engineering.
- Design a system, component or process to meet desired needs.
- Identify, formulate, and solve engineering problems.
- Communicate effectively.
- Recognize of the need for, and the ability to engage in life-long learning.
- Use the techniques, skills, modern engineering tools necessary for engineering practice.

Please answer the following questions regarding the course:

- The textbook was clearly written and appropriate for the course.
- The homework helped me to understand the concepts presented in the course.
- The tests were appropriate in length and content.
- The level of work required in this course was appropriate for the credit given.
- The design project helped me to understand how the fundamental course material is applied in an elementary design problem?

In this course I acquired an understanding of the following topics:

- Finite difference and finite volume methods.
- Spatial discretization and numerical integration.
- Numerical linear algebra.

**Last modified**:

2013-4-29

** **

*Last Modified: 2007-07-24 at 10:04:42*
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