AMATH 574
SLN 1197, MW 3:30 - 4:45, EE1 054
(Prerequisites: AMATH 586 or equivalent)
Conservation Laws and Finite Volume Methods
Instructor:
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Professor
Randall J. LeVeque
Guggenheim 408A
tel: 685-3037
fax: 685-1440
rjl@amath.washington.edu
office hours: T,W 11-12
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Course Description
Theory of linear and nonlinear hyperbolic conservation laws modeling
wave propagation in gases, fluids, and solids. Shock and rarefaction
waves. Finite volume methods for numerical approximation of solutions;
Godunov's method and high-resolution TVD methods. Stability,
convergence, and entropy conditions. Prerequisite: AMath 586 or
permission of instructor.
Textbook
Available at the University Bookstore:
Tentative List of Topics
- Derivation of conservation laws
- Advection and acoustics equations
- Hyperbolicity of linear equations
- Characteristics and Riemann problems
- Finite volume methods in conservation form
- Upwind method, Godunov's method
- Limiters and high-resolution TVD methods
- Use of the CLAWPACK
software, which implements these methods
- Boundary conditions
- Stability and the CFL condition, convergence
- Nonlinear scalar equations: traffic flow, Burgers' equation
- Shocks, rarefaction waves, Rankine-Hugoniot conditions
- Entropy conditions
- Nonlinear systems of conservation laws
- Shallow water equations, Euler equations of gas dynamics
- Finite volume methods for nonlinear systems
- Approximate Riemann solvers
- Extensions to multidimensional problems
Schedule and Homework
Follow links in the table below to obtain a copy of the homework in
PostScript (.ps) or
Adobe
Acrobat (.pdf) format, and also for associated scripts or data files.
| |
Date |
Event |
Homework Problem sets |
| Week 1 |
M, Jan. 3 |
First day of classes |
| Week 2 |
W, Jan. 12 |
Homework 1 due |
hw1 |
| Week 3 |
M, Jan. 17 |
No class: M.L. King Day |
|
F, Jan. 21 |
Extra lecture 3:30 |
| Week 8 |
M, Feb. 21 |
No class: President's Day |