Prerequisites: IT Upper division or graduate student, CS 1113, AEM 4201

Introductory concepts in finite difference and finite volume methods as applied to various ordinary/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.

Textbook: Required: Computational Fluid Dynamics - Vol. 1, 4th edition, Hoffman, EES, ISBN: 0962373109

Summary

This course is focused on the numerical solution of partial differential equations (PDEs) using finite difference and finite volume methods. In the first third of the course students will learn the basic mathematical tools needed to derive and analyze numerical methods to solve PDEs. In the second part of the course students will explore methods to solve parabolic, elliptic and hyperbolic model PDEs. In the final third of the course the methods developed for the model equations will be combined to solve more complex fluid dynamics equations.

Although the focus is fluid dynamics, the material is relevant to the solution of other PDEs and systems of PDEs. This course may be useful to students in mechanical engineering, biomedical engineering, physics, and civil engineering, as well as aerospace engineering and mechanics.

Homework is assigned approximately every other week. The homework generally includes programming problems, which may be completed using Fortran or C++. Matlab is not acceptable for programming assignments, although it may be used for post-processing. Two mid term exams will be given during the semester, but there is no final exam in this course. Instead a final project is assigned. For the project the students will write a computer program to solve a realistic fluid flow problem. The students will also write a report for the project.

The course is aimed at graduate students and advanced undergraduates. Strong mathematics skills, especially linear algebra, are particularly useful, although the necessary mathematics will be reviewed in class. A course in Fortran or C++ is a prerequisite for this course, and the homework assignments and project will include programming.