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 (to access many of these papers or books, you will need to be logged into your SFU Library account).
• Through the Library's "Reserves" page for APMA 930.
• Photocopy from the journal in the library.
• Come see me and ask to borrow my personal copy.

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):5-16, 2006.
  [ A nice historical survey of CFD that is skewed 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):1-34, 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, 210:307-357, 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):10-19, 2009.
  [ A general interest article on CFD and applications. ]
• S. Cannone and S. Friedlander, "Navier: Blow-up and collapse", Notices of the AMS, 50(1):7-13, 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 Navier-Stokes equation", Millennium Prize problem description, Clay Mathematics Institute, 2000.
  [ 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, "Vortices and 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", 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 readable concise treatment of finite difference methods. ]
• D. R. Durran, Numerical Methods for Fluid Dynamics With Applications to Geophysics", Springer, 2010.
  [ A fantastic book with an emphasis on methods for wave propagation problems. ]
• R. Courant, K. Friedrichs and H. Lewy, "On 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, "The 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, "The cell Reynolds number myth", International Journal for Numerical Methods in Fluids, 5:305-310, 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 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, etc. ]
• 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, 2012.
  [ 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(5-6):651-666, 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, 22-30 August, 2006.
  [ 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.
  [ A short and very readable historical overview of convection-diffusion equations, stability, artificial diffusion, and adaptive methods. ]