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)
Notes on boundary layer theory
National Committee for
Fluid Dynamics Films
Lecture notes for incompressible
computational fluid dynamics (CES 715)
N.B. not all
material is included in the notes.
Maple programs
Matlab programs
nonunifgrid.m
convection_diffusion.m
exact_solution.m
scheme.m
fL.m
exact_phi.m
q.m
Assignments
Exams
Nicholas Kevlahan
2010-04-16