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.