School of Meteorology Course

Fall 2003

Computational Fluid Dynamics

METR 5344

Instructor: Prof. Ming Xue

10:30-11:20am, Monday, Wednesday and Friday, 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)

Survey of Numerical Methods used in Mainstream Mesoscale Models (time permitting)

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 short paper. The students will give 20-minute presentations of their results to the class. Students will have access to SOM Metlab workstations and OSCER IBM supercomputer (Sooner).

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.