APMA 930 Readings
Collected below is a list of references for APMA 930, which
can be obtained in one of the following ways:
I have highlighted with a those that I consider to
be "required reading".
- On the web: if there is a link, just click on it (for many, you
will need to be on an SFU machine).
- Through the
Library's "Reserves" page for APMA 930 (you must access this link
through an SFU machine).
- Photocopy from the journal in the library.
- Come see me and ask to borrow my personal copy.
- Introduction to CFD, Historical Background, etc.:
"Going with the flow",
Scientific Computing World, March/April, 2003.
(distributed in class)
fluid dynamics: Science and tool",
Mathematical Intelligencer, 28(1):5-16,
[ A nice historical survey of CFD, skewed a bit towards
compressible flow. It includes brief profiles of
giants such as von Neumann, Lax, Godunov, ... ]
P. J. Roache, "Introduction", Chapter 1 in Fundamentals
of Computational Fluid Dynamics, Hermosa Publishers,
1998. (distributed in class)
- G. Birkhoff,
dynamics", SIAM Review,
[ An excellent review of analytical and computational fluid
- L. F. Richardson,
approximate arithmetical solution by finite differences of
physical problems involving differential equations, with an
application to the stresses in a masonry dam",
Philosophical Transactions of the Royal Society of
London A, 210:307-357, 1911.
[ One of the first numerical solution method for a PDE, with
some very intriguing historical anecdotes. ]
- A. Quarteroni,
models in science and engineering", Notices of the
AMS, 56(1):10-19, 2009.
[ A general interest article on CFD and
- S. Cannone and S. Friedlander,
and collapse", Notices of the AMS,
[ An historical overview of Navier's contribution to fluid
- Governing Equations and Mathematical Issues:
P. Wesseling, "The basic equations of fluid
dynamics", Chapter 1 in
of Computational Fluid Dynamics, Springer, 2001.
(distributed in class)
- C. L. Fefferman,
& smoothness of the Navier-Stokes equation",
Millennium Prize problem description, Clay Mathematics
[ Open problems in existence, smoothness, and regularity
of solutions to the Navier-Stokes equations in 3D that could
potentially net you $1 million! ]
- C. E. Wayne,
two-dimensional fluid motion",
Notices of the AMS, 58(1):10-19, 2011.
[ Mathematical issues behind motion of vortices. ]
- C. Y. Wang, "Exact solutions of the steady-state Navier-Stokes
equations", Annual Review of Fluid Mechanics, 23:159-177
1991. (hardcopy only)
[ A comprehensive review of the existing analytical solutions. ]
- R. M. Kiehn, "Some closed
form solutions to the Navier Stokes equations",
[ Some of these exact solutions involving interesting
bifurcation behaviour which might form the basis for a
- Finite Difference Methods for Linear Problems:
- K. W. Morton and D. F. Mayers,
Solution of Partial Differential Equations: An
Introduction", second edition, Cambridge University
[ A great treatment of finite difference methods. ]
R. Courant, K. Friedrichs and H. Lewy,
the partial difference equations of mathematical
physics", IBM Journal of
Research and Development, 11(2):215-234,
March 1967 (translation of the original German article from
Mathematische Annalen, 100:32-74, 1928).
[ A seminal paper that introduced the concept of stability and
CFL number. ]
- E. Sousa,
controversial stability analysis",
Applied Mathematics and Computation, 145:777-794, 2003.
[ A fascinating account of the history behind the stability of
the FTCS method applied to the advection-diffusion. He
explains how past errors in the analysis, although corrected,
still appear in the recent literature. ]
H. D. Thompson, B. W. Webb and J. D. Hoffman,
cell Reynolds number myth", International Journal
for Numerical Methods in Fluids, 5:305-310,
[ They study in detail the (ir)relevance of the cell Reynolds
number criterion for the FTCS scheme applied to the
advection diffusion equation. ]
- Incompressible Fluid Flow:
P. Colella and E. G. Puckett,
Numerical Methods for Fluid Flow, draft notes, 1998.
[ Contains material on numerical methods for both
incompressible and compressible flows. ]
B. Seibold, "A
compact and fast Matlab code solving the incompressible
Navier-Stokes equations on rectangular domains",
unpublished report, MIT, March 31, 2008.
[ This paper describes a short and efficient code that
solves the 2D incompressible NSEs using a split-step
projection method on a staggered grid (explicit advection,
implicit diffusion). By default, it is set up to solve the
driven cavity problem. ]
- H. P. Langtangen, K.-A. Mardal and Ragnar Winther, "Numerical
methods for incompressible viscous flow", Advances
in Water Resources, 25(8-12):1125-1146, 2002.
[ A fairly comprehensive review that covers many of the
algorithms that we'll see in the course. ]
- P. J. Roache, "The Legitimacy of the Poisson
Pressure Equation", Chapter 12 in Fundamentals of
Computational Fluid Dynamics, Hermosa
Publishers, 1998. (distributed in class)
[ He addresses a controversy on issues surrounding the
pressure Poisson equation, boundary conditions,
- P. M. Gresho, "Incompressible
fluid dynamics: Some fundamental formulation issues",
Annual Review of Fluid Mechanics, 23:413-453,
1991. (distributed in class)
[ A much more detailed study of formulation issues hinted at
by Roache (1998, Ch. 12). ]
- Flow in Porous Media:
J. E. Aarnes, T. Gimse and K.-A. Lie,
"An introduction to the numerics of flow in porous media
using Matlab", in Geometric Modelling, Numerical
Simulation, and Optimization: Applied Mathematics at
SINTEF, Part II, eds. G. Hasle, K.-A. Lie and E. Quak,
pp. 265-306, 2007.
[ A clear discussion of simple finite volume and finite
element methods for reservoir simulation problems, in
particular the "black-oil model" using an IMPES method. The
article includes Matlab code. ]
- J. D. Logan, Transport modeling in hydrogeochemical
systems, Springer, 2000. (distributed in class)
[ Chapter 5 has a very nice introduction to Darcy's Law and
Richards equation for unsaturated flow. This book has a
wealth of interesting project ideas. ]
K. Roth, "Soil Physics"
(lecture notes), Institute
of Environmental Physics, University of Heidelberg, Autumn 2009.
[ These notes contain a nice physical background for flow in
porous media. ]
- B. H. Gilding,
mathematical analysis of the Richards equation",
Transport in Porous
Media, 6(5-6):651-666, 1991.
[ An extensive overview of recent theoretical results on
the Richards equation (existence, uniqueness, regularity,
- D. A. Nield and A. Bejan,
in Porous Media,
Springer, third edition, 2006.
- Nonlinear Wave Propagation:
- R. J. LeVeque,
volume methods for hyperbolic problems,
Cambridge University Press, 2002.
[ A great textbook, with code available at the
CLAWPACK web site. ]
R. J. LeVeque,
propagation software, computational science and reproducible
research", in Proceedings of the International
Congress of Mathematicians, Madrid, Spain, 22-30
[ He discusses the importance of software development in the
context of computational science research. ]
- M. Stynes, "Numerical methods for convection-diffusion
problems" or "The 30 years war", in Proceedings of the 20th
Biennial Conference on Numerical Analysis, University of
Dundee, Scotland, 2003. (hardcopy only)
[ A short and very readable historical overview of
convection-diffusion equations, stability, artificial
diffusion, and adaptive methods. ]
Last modified: Thu Feb 24 2011