AMATH 574
SLN 10212, MW 3:30-4:50, CDH 125
(Prerequisites: AMATH 586 or equivalent)

Conservation Laws and Finite Volume Methods

Instructor:
Professor Randall J. LeVeque
Condon Hall 732
tel: 685-3037
fax: 685-1440
rjl at amath.washington.edu
office hours: MW 2:30-3:30 or by appointment

Lectures: MW 3:30 - 4:50 and some Fridays 3:30-4:20 (see schedule below)
Condon Hall 125

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.

More course description

Textbook

Available at the University Bookstore:

Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.
Errata for the book

For background material:

AMath 585-6 course notes are available at the Profession Copy Center on the Ave.
On-line version for reference (restricted access)

Software

We will be using the CLAWPACK software.

If you are working on the amath computer system, the library routines and compiled .o files are available in /home/claw/CLAW so you can set environment variables to point there rather than downloading and installing everything.
Otherwise, follow instructions from the Download page from the main CLAWPACK menu.

Tentative Outline

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
Source terms
Extensions to multidimensional problems

Homework assignments

Schedule (tentative -- will be updated)

	Date	Event	Suggested reading
Week 1	W, Jan. 3	First day of classes	Chapter 1 and 2.1-2.5
Week 2	M, Jan. 8		Sections 2.6-2.11, 3.1-3.8
	W, Jan. 10		Sections 3.9, 4.1-4.9
	F, Jan. 12		Sections 4.9-4.14
Week 3	M, Jan. 15	No class: M.L. King Day
	W, Jan. 17		Chapter 5, Sections 6.1-6.4
	F, Jan. 19		Sections 6.5-6.15
Week 4	M, Jan. 22		Chapter 7 and Sections 11.1-11.4
	W, Jan. 24		Sections 11.1-11.10
	F, Jan. 26		Sections 11.11-11.14
Week 5	M, Jan. 29		Chapter 12
	W, Jan. 31
	F, Feb. 2		Section 12.12 and 13.1
Week 6	M, Feb. 5		Section 13.2-13.7
	W, Feb. 7		Sections 13.8-13.12
	F, Feb. 9
Week 7	M, Feb. 12
	W, Feb. 14	No class
	F, Feb. 16	No class
Week 8	M, Feb. 19	No class: President's Day
	W, Feb. 21	No class
	F, Feb. 23	No class
Week 9	M, Feb. 26
	W, Feb. 28
	F, Mar. 2
Week 10	M, Mar. 5
	W, Mar. 7
	F, Mar. 9
Finals Week

Instructor:	Professor Randall J. LeVeque Condon Hall 732 tel: 685-3037 fax: 685-1440 rjl at amath.washington.edu office hours: MW 2:30-3:30 or by appointment
Lectures:	MW 3:30 - 4:50 and some Fridays 3:30-4:20 (see schedule below) Condon Hall 125