JianGuo Liu : Math 226 Numerical Methods for Partial Differential Equations
Class hours: MWF 1:302:20 Physics 119
Office hours: MWF 11:0012:00 Physics 295, Tel: 6602841
Email: jliu "at " math.duke.edu,
http://www.math.umd.edu/~jliu"
Course Description:
Duke Online Course Synopsis Handbook:
Numerical solution of hyperbolic conservation laws.
Conservative difference schemes, modified equation analysis and Fourier analysis,
LaxWendroff process. Gas dynamics and Riemann problems.
Upwind schemes for hyperbolic systems. Nonlinear stability,
monotonicity and entropy; TVD, MUSCL, and ENO schemes for scalar laws.
Approximate Riemann solvers and schemes for hyperbolic systems.
Multidimensional schemes. Adaptive mesh refinement.
Finite difference and spectral methods for timedependent
problems. Hyperbolic and parabolic systems, initial and
initialboundary value problems of hyperbolic and parabolic
types. Stability and convergence theories for linear and nonlinear
problems. Finite difference methods for elliptic problems.
Textbook:
Reference:
Numerical methods for PDE:
Lloyd N. Trefethen: Spectral Methods in MATLAB (Software, Environments, Tools), SIAM, 2001
Stig Larsson and Vidar Thomee: Partial Differential Equations with Numerical Methods (Texts in Applied Mathematics),
SpringerVerlag, 2005
William L. Briggs, Van Emden Henson, and Steve F. McCormick: A Multigrid Tutorial,
SIAM, 2000
Bengt Fornberg: A Practical Guide to Pseudospectral Methods (Cambridge Monographs on Applied and Computational Mathematics), 1998
Alfio Quarteroni and Alberto Valli: Numerical Approximation of Partial Differential Equations (Springer Series in Computational Mathematics), 1997
K. Eriksson, D. Estep, P. Hansbo, and C. Johnson: Computational Differential Equations,
Cambridge University Press, 1996
Mathematical and Numerical Analysis on Compressible Flow:
P.D. Lax:
Hyperbolic systems of conservation laws and the mathematical theory of
shock waves (1973);
J. Smoller:
Shock waves and reactiondiffusion equations, 2nd ed. (1994);
E. Godlewski and PA Raviart:
Hyperbolic systems of conservation laws (1991);
E. Godlewski and PA Raviart:
Numerical approximation of hyperbolic systems of conservation laws
(1996);
P.L. Lions:
Mathematical Topics in Fluid Mechanics, v.2. Compressible Models (1996)
B. Gustafsson, HO Kreiss, J. Oliger:
Time Dependent Problems and Difference Methods (1995)
H.O. Kreiss and J. Lorenz:
InitialBoundary Value Problems and the NavierStokes equations (1989)
CFD:
Ch. Hirsch:
Numerical computation of internal and external flows,
v.1. Fundamentals of numerical discretization (1988),
v.2. Computational methods for inviscid and viscous flows. (1990);
R.D. Richtmyer and K.W. Morton:
Difference methods for initialvalue problems, 2d ed. (1967);
C. Canuto, et al.:
Spectral Methods in Fluid Dynamics (1988)
R. Peyret and T.D. Taylor:
Computational Methods for Fluid Flow (1985)
C.A.J. Fletcher:
Computational Techniques for Fluid Dynamics (1991)
Basic Numerics, Scientific Computing, and
Software Packages:
Numerical Recipes in Fortran or in C, Cambridge University Press
H.O. Kreiss:
Numerical Methods for Solving TimeDependent Problems
for Partial Differential Equations (1978)
J.C. Strikwerda:
Finite Difference Schemes and Partial Differential
Equations (1989)
Morton, Mayers:
Numerical Solution of Partial Differential Equations
Scientific Computing
MAPL660, Fall 98,
MAPL661, Spring 99
Computational Fluid Dynamics,
MAPL698b, Fall 99
Financial Modeling & Simulation,
MAPL699, Spring 00
My Papers on CFD
 Introduction to Compressible Flow
rding
 Mathematical Theory
 Numerical Methods
 More applications (depending in part on the interests of students)
 Web Sites Links:
 Fluid Mechanics:

(ASME) The American Society of Mechanics Engineers
International
(AIAA) The American Institute of Aeronautics and Astronautics
(APS) The American Physical Society, Division of Fluid
Dynamics
Yahoo: Fluid Dynamics Index
Fluid Mechanics Related Web Pages
ICASE Fluid Mechanics Highlights
 Flow Image Collections:

Fluid Dynamics Picture of the Week
(contains many other links to fluid dynamics topic areas).
National
University of Singapore T.T.
Lim's home page. Spectacular images of fluid flows, including a