Winter 2015: ATMS 582

Advanced Numerical Modeling of Geophysical Flows

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


Instructor: Professor Dale Durran
drdee@uw.edu
Office hours: Tuesday 2:30-3:30 and by appointment.

Textbook: Durran, D.R., 2010: Numerical Methods for Fluid Dynamics: With Applications in Geophysics. 2nd Ed. Springer-Verlag.

The book is available by chapters for free as pdfs via a subscription through the UW library. That subscription also entitles students to buy $25 paperback copies. To access these priviliges, connect here via a UW computer, and click 'Read Online'.

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, particulary weather and climate. This course is nominally offered every-third year. The class builds on material covered in ATMS 581/AMATH 586, although some familiarity with numerical methods for the solution of partial differential equations is generally adequate preparation.


Homework

Read Sections 3.3.2 and 3.3.3 (pp. 109-114) by Friday 1/9
Exercise 1: due Friday 1/23. Matlab files: fig3_7, first_biased, second_centered
Read Sections 4.3 and 4.3.1 (pp. 169-173) by Wednesday 1/21 and email me one discussion question by 8 AM on the 21st.( Note there is a typo in the footnote on p. 170. Errata is here.

Exercise 2: due Friday 2/6. Matlab files: SW_stagger.m, forward_backward.m, smooth.m
Read Section 5.10.1 (pp. 271-273) by Wednesday 2/4 and email me one discussion question by 8 AM on the 4th

Exercise 3 (take home midterm): due Friday 2/20. Matlab files: starting_point.m, Lax_Wendroff.m
Osher limiter, Sweby limiter, phase speed errors in non-symmetric distribution

Exercise 4: due Friday 3/6. Matlab files: Burger_starting_point.m,
Solutions at t=0.2, L2 norms, L2 norms of the error

Hand in a short description of your project on Friday 2/27

Short project due by 8 AM Wednesday 3/18.

Course Outline

Review: Differential-Difference Equations for the Scalar Wave Equation

Further Considerations in Finite Difference Approximations

Finte-Volume Methods

Spectral and Pseudo-Spectral Models

The Discontinuous Galerkin and Spectral Element Methods

Semi-Lagrangian Methods

Strategies for Nonhydrostatic (Convection Permitting) Modelling

 


Grading:  The grade will be based on a short project and short bi-weekly 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 homeworks. The project will ideally be something related to your research.