School of Meteorology Course

Announcement - Fall 2001

Computational Fluid Dynamics

METR 5344

Instructor: Prof. Ming Xue

10:30-11:45am, Tuesday and Thursday, SEC1410

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: Computational Fluid Mechanics and Heat Transfer by J.C. Tannehill, D. A. Anderson and R. H. Pletcher.

Reference Book: 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) or a similar mesoscale or cloud model, perform numerical experiments and prepare a paper. First drafts will be peer reviewed by two fellow students. The students will give 20-minute presentations of their results to the class. Students will have access to Cray J90 Supercomputer and SOM workstations.

If you have any question, please contact me at 325-6037, mxue@ou.edu or see me in SEC Rm. 1158.

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.