Math 745    Mathematical and Computational Fluid Dynamics   Winter 2010

DR. N. KEVLAHAN

Office: HH 324, Tel: x23412
Email: kevlahan@mcmaster.ca
Office hours: by appointment

Tuesdays and Fridays, 14:00-15:15 HH 312

## Purpose of the course

The purpose of this course is to introduce the equations and fundamental theorems of mathematical fluid dynamics, and to then to
derive practical numerical techniques that can be used to solve a wide variety of fluid problems.  In addition, the numerical techniques you will learn can also be applied to the partial differential equations one encounters in many other fields of science and engineering.

This course will be given in the form of two six-week modules, as follows:

Mathematical Introduction to Fluid Mechanics (CES 716)
We derive the Euler and Navier-Stokes equations from the first principles of continuum mechanics. Mathematical properties of these systems of equations are discussed, such as the boundary conditions, potential and rotational flow and representation of the equations in different coordinate systems. We also briefly consider shocks, boundary layers and turbulence as well as the limits of small and large Reynolds number. Finally, we survey analytical solutions of the Euler and Navier-Stokes equations.

Incompressible Computational Fluid Dynamics (CES 715)
We introduce techniques for the numerical solution of partial differential equations, with a special emphasis on fluid dynamics.  We focus on finite volume techniques (as a special case of finite elements).  We are particularly interested in equations with discontinuities (interface problems), efficient treatment of boundary layers and high Reynolds number flows.  Fundamental aspects such as local and global truncation error, consistency, convergence, stability, non-uniform grids and numerical oscillations are introduced in the context of specific problems. The module finishes with the derivation of a full staggered grid discretization of the incompressible Navier--Stokes equations (with general boundary conditions and pressure correction split step).  Matlab computer codes are used throughout the course to illustrate the material.

## Text

The main text for this course is Principles of computational fluid dynamics by P. Wesseling (Springer, 2001).

Course outline

Course notes

Lecture notes for mathematical fluid dynamics (CES 716) (updated for 2010)

N.B. not all material is included in the notes.

## Matlab programs

nonunifgrid.m
convection_diffusion.m
exact_solution.m
scheme.m
fL.m
exact_phi.m
q.m

## Assignments

 Assignment Solutions Assignment 1 Assignment 1 Solutions Assignment 2 Assignment 2 Solutions Assignment 3 Assignment 3 Solutions Assignment 4 Assignment 4 Solutions

## Exams

 Exam Solutions Exam 1 (CES 716) Exam 1 Solutions Exam 2 (CES 715)

Nicholas Kevlahan

2010-04-16