Jian-Guo Liu : Math 226 Numerical Methods for Partial Differential Equations
Class hours: MWF 1:30-2:20 Physics 119
Office hours: MWF 11:00-12:00 Physics 295, Tel: 660-2841
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,
Lax-Wendroff 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 time-dependent
problems. Hyperbolic and parabolic systems, initial and
initial-boundary 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),
Springer-Verlag, 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
PDE:
Lawrence C. Evans: Partial Differential Equations (Graduate Studies in Mathematics, V. 19) 1998
Walter A. Strauss: Partial Differential Equations: An Introduction, Wiley, 1992
Fritz John: Partial Differential Equations (Applied Mathematical Sciences), Springer; 4th ed., 1991
Compressible Flow:
R. Courant and K.O. Friedriches:
Supersonic Flow and Shock Waves(1948);
J.D. Anderson:
Modern compressible flow with historical perspective, 2nd ed., (1990);
W.G. Vincenti and C.H. Kruger:
Introduction to physical gas dynamics (1965);
L. Landau and E. Lifschitz:
Fluid Mechanics (1959);
D.J. Acheson:
Elementary Fluid Dynamics (1990).
A.J. Chorin and J.E. Marsden:
A Mathematical Introduction to Fluid Mechanics
G. B. Whitham:
Linear and nonlinear waves (1974);
M. Van Dyke:
An Album of Fluid Motion (1982);
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 reaction-diffusion equations, 2nd ed. (1994);
E. Godlewski and P-A Raviart:
Hyperbolic systems of conservation laws (1991);
E. Godlewski and P-A 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, H-O Kreiss, J. Oliger:
Time Dependent Problems and Difference Methods (1995)
H.-O. Kreiss and J. Lorenz:
Initial-Boundary Value Problems and the Navier-Stokes 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 initial-value 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 Time-Dependent 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