ATM S 581, Autumn Quarter 2001
Numerical Modeling of Atmospheric Flows
606 Atmospheric Sciences Bldg., 543-7440
durrand@atmos.washington.edu
Lectures:MWF, 2:30 - 3:20, 610 ATG
Textbook: Durran, D.R., 1999: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer-Verlag.
Purpose of Course:
To obtain a thorough understanding of the basic numerical techniques that form the foundation for the computer models commonly used to stimulate atmospheric motions. The focus is on fundamental numerical methods used to simulate low-viscosity fluid motions. We will not delve into the details of individual atmospheric models; rather we will examine prototype problems such as tracer transport, shallow-water waves, and internal waves in a density stratified fluid.
Methodologies:
The theoretical properties of each basic numerical technique will be illustrated by constructing simple models using MATLAB. Some modeling results will be presented as demonstrations in class; other modeling exercises will be assigned as homework.
Course Outline:
- The difficulty of simulating low-viscosity flow.
- Overview of numerical solution strategies.
- Accuracy, consistency, stability and convergence
- Time differencing.
- Spatial differencing
- The combined effects of time and space differencing.
- General properties of series expansion methods
- The spectral method
- The pseudo-spectral method
- Spherical Harmonics
- The necessity of conservation form when the solution is discontinous.
- Flux-corrected transport
- Multi-dimensional scalar advection
- The shallow-water system