School of Meteorology Course

Announcement - Spring 2000

Computational Fluid Dynamics I

METR 5344

Instructor: Prof. Ming Xue

11:30-12:20am, MWF, SEC1243

Credit: 4 hours

General Information: This course teaches the background theories and numerical methods for solving fluid dynamics problems. It is the foundation of numerical modeling and numerical weather prediction.

Prerequisites: Math 3123 (Engineering Math II or equivalent); ENGR 3723 (Numerical Methods or equivalent); a course in fluid mechanics/dynamics (e.g., ENGR 3223, METR 3113 and/or 5113); ability to program in Fortran; familiarity with the UNIX operating system (last two requirements are imperative).

Text: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics by Dale R. Durran

Practical Issues of High Performance Computing computer architectures; code design and optimization; parallel and vector constructs; limiting factors and constraints on simulation studies; guidelines for writing maintainable code. Background of numerical weather prediction. (2/3 week)

Theory of Partial Differential Equations classification; canonical forms; linear vs nonlinear problems; characteristics; well posed problems (1 week)

Fundamentals of Finite Difference Methods consistency; stability; convergence and order of accuracy; methods for obtaining discretizations (2 weeks)

Classical Problems and Methods implicit and explicit methods for parabolic, hyperbolic, and elliptic problems; directional splitting; dissipation and dispersion errors; practical measures of convergence and accuracy. (5 weeks)

Basic Hydrodynamics Burgers equation and nonlinear steepening; filtering; the shallow water equations; grid staggering, nonlinear instability, conservation constraints. (2 weeks)

Boundary Conditions (BC) for Hyperbolic Problems/Systems - Options of BC, wave-permeable radiation conditions, well-posedness of BC; PE and vorticity/streamfunction formulations. (2 weeks)

Semi Lagrangian and Spectral/Pseudo Spectral Methods philosophy and formulation; application to 1 D problems; FFT and spectrum transform method. (3 1/3 weeks)

Course Grading: 3 Hour Exams 45%

Computer Problems 30%

Term Project * 25%

*Students will research an approved topic using the Advanced Regional Prediction System (ARPS), perform numerical experiments and prepare a paper. First drafts will be peer reviewed by two fellow students. Students will have access to Cray J90 Supercomputer and workstations of the ECAS Lab.

If you have any question, please contact me at 325-6037, mxue@ou.edu or see me in SEC Rm. 1114.

Any student in this course who has a disability that may prevent him or her from fully demonstrating their potential should contact the School of Meteorology (325-6561) immediately to arrange for appropriate accommodations that will ensure your full participation and facilitate your educational opportunity.