Winter 2004: ATMS 582

**Advanced Numerical Modeling of Geophysical Flows**

MWF 10:30-11:20, Room ATG 610

*Instructor:*
Professor Dale Durran

606 ATG, 543-7440, durrand@atmos.washington.edu

Office hours: Tuesday 2:00-3:00, Thursday 2:00-3:00

*Textbook:*
Durran, D.R., 1999: *Numerical Methods for Wave Equations in
Geophysical Fluid Dynamics*. Springer-Verlag.

*Overview:*
The purpose of the course is to obtain a deeper understanding of the
basic numerical techniques that form the foundation for the computer
models commonly used to simulate geophysical flows. This course is
taught every-other year and builds on material covered in ATMS
581/AMATH 586.

*Homework*

*Course Outline
*

*Further
Considerations in Finite Difference Approximations
*

- Staggered meshes
- Stability constraints in simulations of multi-dimensional waves
- Splitting
into fractional steps

*Spectral Models on
the Sphere
*

- Spherical
Harmonic Functions
- Elimination of the Pole Problem

*Approximate
Solutions to Conservation Laws
*

- Improving
upstream differencing
- Flux limiter methods
- Slope limiter methods

- Improving centered schemes
- ENO (essentially nonoscillatory) methods

*Approximating Open
(Wave-Permeable) Boundaries*

- The 1D shallow-water system and well-posed boundary conditions
- Stability conditions for initial-boundary-value problems
- Extensions
to two-dimensional shallow-water flow

- Extensions to two-dimensional stratified flow

Semi-Lagrangian Methods

- The scalar advection equation
- Forcing the Lagrangian frame
- Comparison with the method of characteristics

*Grading:*
The grade will be
based on four homework assignments, one of which will be identified as
a take-home midterm that must be done *independently*.
You may work with other students on the other three homeworks.