### Computational Fluid Dynamics

#### ME 61400 / 3 Cr. (3 Class)

Application of finite difference methods, finite element methods, and the method of characteristics for the numerical solution of fluid dynamics problems. Incompressible viscous flows: vorticity transport equation, stream function equation, and boundary conditions. Compressible flows: treatment of shocks, implicit and explicit artificial viscosity techniques, and boundary conditions. Computational grids.

**Available Online:** No

**Credit by Exam:** No

**Laptop required:** No

**Prerequisites/Co-requisites:**

P: ME 58100 or equivalent; ME 50900 or 51000 or equivalent; or consent of instructor.

**Coordinator: **Akin Ecer, Ph.D.

##### Textbooks

Anderson, J. D., Computational Fluid Dynamics - The Basics with Applications, McGraw-Hill, New York, 1995.

##### Goals

To introduce the student to the basics of computational fluid dynamics (CFD). The main focus will be on the use of finite difference methods for numerical integration of partial differential equations and governing equations of fluid dynamics and heat transfer will be inroduced and considered. One main theme will be the accuracy and stability of the numerical schemes employed for the solution of CFD problems. Explicit and implicit schemes will be studied.

##### Outcomes

**After completion of this course, the students should be able to:**

- Derive the Navier stokes equations.
- Distinguish the properties of partial differential equations for compressible and incompressible flows.
- Determine the accuracy of a difference algorithm.
- Determine the stability of a difference algorithm.
- Develop a computer code to study the accuracy and stability of an algorithm for an incompressible flow problem.
- Develop a computer code to study the accuracy and stability of an algorithm for a compressible flow problem.
- Evaluate an accuracy and stability of a given algorithm.
- Review a technical paper describing a specific algorithm.
- Review a technical manual of a commercial flow code.

##### Topics

- PDE equations and model equation (3 lectures)
- Introduction to MATLAB (2 lectures)
- Finite-difference approximations (5 lectures)
- Finite-difference methods for model equations (11)
- Governing equations (2 lectures)
- Numerical methods for incompressible flows (7 lectures)
- Numerical methods for compressible flows (8 lectures)
- Grid Generation Techniques (5 lectures)
- Special topics (2 lectures)