ATM S 582, Winter Quarter 2001

Numerical Modeling of Atmospheric Flows II

Instructor: Professor Dale Durran
606 Atmospheric Sciences Bldg., 543-7440
durrand@atmos.washington.edu

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

Textbook: Durran, D.R., 1998: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer-Verlag.

Purpose of Course:

Gain a deeper understanding of the basic numerical techniques that form the foundation for the computer models commonly used to simulate wave-like flow with particular emphasis on atmospheric applications.

Format of Course:This course is offered every other year and is graded credit/no-credit. Credit will be assigned on the basis of a project and two short homework assignments. No programming will be required to complete the homework. There will be no exams. Students using numerical models in their research are encouraged to select a project related to that work. Additional topics will be suggested for those students not directly involved in numerical modeling.

Course Outline:

Further topics in finite-difference methods

• Staggered meshes
• Fractional step methods

• Diffusion, sources and sinks

Finite Volume Methods

• The necessity of conservation form when the solution is discontinuous
• Stability and accuracy for problems with discontinuous solutions.
• Flux-corrected transport
• Flux-limiter methods

Approximations at an open boundary

• The 1D shallow-water system and well-posed boundary conditions
• Concept of a wave-permeable boundary condition
• Stability conditions for initial-boundary-value problems
• Extensions to two-dimensional shallow-water flow.
• Extensions to two-dimensional stratified flow.

Efficient simulation of systems with fast and slow waves

• The projection method
• Semi-implicit method
• Time-split methods

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