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

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.

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Homework

Exercise 1 (nothing yet)

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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 
  1. Flux limiter methods 
  2. 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

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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.