Fall 2012

Math 375

Math 579

Computational Fluid Mechanics - Math 579 - 002: Fall 2012


The aim of this course is to provide the student with the analytical tools needed to find accurate and efficient numerical solutions of various flow phenomena. Studying successful examples of numerical methods for incompressible and compressible flows we will learn how to analyze the mathematical foundations for efficient and accurate discrete approximations to functions, and various Ordinary and Partial Differential Equations. As there is no general numerical method which is effective for all problems, it is critically important to understand the mathematical properties (benefits, limitations, and pathologies), of various approximations, so that the one which is most accurate and efficient for a particular problem may be chosen and correctly implemented. Throughout we will give examples of efficient methods from the literature.

The course will consist of lectures and a guided, individual, computing project. The Lecture topics are given below. During the first part of the course, weekly homework sets will focus on fundamentals of numerical analysis, and the development of algorithms and programs that will be useful for the latter part of the course. In the second part of the class, students will develop two programs, one to compute incompressible flow in a two-dimensional geometry and one to compute one-dimensional compressible flow with shocks. Topics for the individual projects will be chosen in consultation with the instructor. Projects related to dissertation research are strongly encouraged, but it should be kept in mind that they must be completed within the time span of the course. Typically the project will involve the numerical solution of a particular flow pheonmena (or flow in a particular geometry), a detailed analysis of the chosen method, and error analysis of computed results.

The course is intended for mathematicians, engineers, physicists and computer scientists.

Time and place: 09.30-10.45, SMLC-352



Files for hwk 2 and proj 1

SBP example

Burger example

Handouts, homework and exams: