APMA 930 Readings
Collected below is a list of references for APMA 930, which
can be obtained in one of the following ways:
 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.
I have highlighted with a those that I consider to
be "required reading".
 Introduction to CFD, Historical Background, etc.:


R. Girvan,
"Going with the flow",
Scientific Computing World, March/April, 2003.
(distributed in class)

B. Koren,
"Computational
fluid dynamics: Science and tool",
Mathematical Intelligencer, 28(1):516,
2006.
[ 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,
"Numerical fluid
dynamics", SIAM Review,
25(1):134, 1983.
[ An excellent review of analytical and computational fluid
dynamics. ]
 L. F. Richardson,
"The
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, 210:307357, 1911.
[ One of the first numerical solution method for a PDE, with
some very intriguing historical anecdotes. ]
 A. Quarteroni,
"Mathematical
models in science and engineering", Notices of the
AMS, 56(1):1019, 2009.
[ A general interest article on CFD and
applications. ]
 S. Cannone and S. Friedlander,
"Navier: Blowup
and collapse", Notices of the AMS,
50(1):713, 2003.
[ An historical overview of Navier's contribution to fluid
mechanics. ]
 Governing Equations and Mathematical Issues:


P. Wesseling, "The basic equations of fluid
dynamics", Chapter 1 in
Principles
of Computational Fluid Dynamics, Springer, 2001.
(distributed in class)
 C. L. Fefferman,
"Existence
& smoothness of the NavierStokes equation",
Millennium Prize problem description, Clay Mathematics
Institute, 2000.
[ Open problems in existence, smoothness, and regularity
of solutions to the NavierStokes equations in 3D that could
potentially net you $1 million! ]
 C. E. Wayne,
"Vortices and
twodimensional fluid motion",
Notices of the AMS, 58(1):1019, 2011.
[ Mathematical issues behind motion of vortices. ]
 C. Y. Wang, "Exact solutions of the steadystate NavierStokes
equations", Annual Review of Fluid Mechanics, 23:159177
1991. (hardcopy only)
[ A comprehensive review of the existing analytical solutions. ]
 R. M. Kiehn, "Some closed
form solutions to the Navier Stokes equations",
arXiv:physics/0102002, 2001.
[ Some of these exact solutions involving interesting
bifurcation behaviour which might form the basis for a
project. ]
 Finite Difference Methods for Linear Problems:

 K. W. Morton and D. F. Mayers,
Numerical
Solution of Partial Differential Equations: An
Introduction", second edition, Cambridge University
Press, 2005.
[ A great treatment of finite difference methods. ]

R. Courant, K. Friedrichs and H. Lewy,
"On
the partial difference equations of mathematical
physics", IBM Journal of
Research and Development, 11(2):215234,
March 1967 (translation of the original German article from
Mathematische Annalen, 100:3274, 1928).
[ A seminal paper that introduced the concept of stability and
CFL number. ]
 E. Sousa,
"The
controversial stability analysis",
Applied Mathematics and Computation, 145:777794, 2003.
[ A fascinating account of the history behind the stability of
the FTCS method applied to the advectiondiffusion. 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,
"The
cell Reynolds number myth", International Journal
for Numerical Methods in Fluids, 5:305310,
1985.
[ 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,
Modern
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
NavierStokes 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 splitstep
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(812):11251146, 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,
etc. ]
 P. M. Gresho, "Incompressible
fluid dynamics: Some fundamental formulation issues",
Annual Review of Fluid Mechanics, 23:413453,
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. 265306, 2007.
[ A clear discussion of simple finite volume and finite
element methods for reservoir simulation problems, in
particular the "blackoil 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,
"Qualitative
mathematical analysis of the Richards equation",
Transport in Porous
Media, 6(56):651666, 1991.
[ An extensive overview of recent theoretical results on
the Richards equation (existence, uniqueness, regularity,
etc.) ]
 D. A. Nield and A. Bejan,
Convection
in Porous Media,
Springer, third edition, 2006.
 Nonlinear Wave Propagation:

 R. J. LeVeque,
Finite
volume methods for hyperbolic problems,
Cambridge University Press, 2002.
[ A great textbook, with code available at the
CLAWPACK web site. ]

R. J. LeVeque,
"Wave
propagation software, computational science and reproducible
research", in Proceedings of the International
Congress of Mathematicians, Madrid, Spain, 2230
August, 2006.
[ He discusses the importance of software development in the
context of computational science research. ]
 M. Stynes, "Numerical methods for convectiondiffusion
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
convectiondiffusion equations, stability, artificial
diffusion, and adaptive methods. ]

Last modified: Thu Feb 24 2011
