Math/Physics 365-Computational Fluid Dynamics-Spring 2000

FIG1: [STILL image] Contours of constant density in heated subsonic (Mach 0.8) round jet. Flow is left to right
with jet axis along lower boundary. (Pruett, AIAA Journal, to appear.)

FIG2: [MOVIE--click image to play] Contours of constant vorticity in an incompressible free shear layer. Flow is left to right. Motion shows roll-up of layer into vortex street and subsequent pairing of adjacent vortices. Computed by Kim and Moin algorithm (J. Computational Physics, 1985) in High-Performance Fortran.



OVERVIEW: The motion of fluids holds both aesthetic and practical fascination for humans. The science of fluid mechanics provides insight into phenomena as diverse as wave action, ocean circulation, weather patterns, the destructive power of tornados and hurricanes, the science of flight, shock waves, the droplet pattern in a half-empty wine glass, the laminar-turbulent transition of a smoke plume rising from a cigarette, blood flow in the heart, and the accretion of galaxies. Because of the complicated nature of the Navier-Stokes equations that govern fluid motions, prior to the second half of the 20th Century, fluid dynamicists could rely only upon simplified theories corroborated by physical experiments to explain and predict fluid-flow phenomena. With the advent of the digital computer, numerical simulation joined theory and experiment in the arsenal of scientific techniques that can be brought to bear in unraveling the mysteries of fluid flow. To date, the quest for a virtual wind tunnel to replace the physical wind tunnel has been somewhat illusory. Nevertheless, with continuing advancements in both computer technology and algorithmic efficiency, computational fluid dynamics has emerged as a powerful and (in the right hands) trustworthy tool for the design of spacecraft, aircraft, and automobiles. In the future, numerical simulation will become ever more important as an emerging "key technology." Say the authors of our text: "The numerical simulation of physical phenomena requires the observations and models of the natural scientist, the technical expertise of the engineer, the numerical methods of the mathematician, and the modern techniques and computers of the computer scientist." This course has been specifically designed as an integral part of JMU?s and NCCU?s collaborative NSF-funded computational-science track to help you--the student--develop and hone the triad of skills that comprise a solid foundation in computational science: modeling of physical phenomena, numerical methods, and scientific visualization.

PREREQUISITES: Math 237, Math 238 (formerly 301E), Math/Phys. 265, and Phys. 340

Dave Pruett
Burruss 018
Dorn Peterson
Miller 126
Jim Sochacki
Burruss 113

PRIMARY TEXT: Numerical Simulation in Fluid Dynamics: A Practical Introduction by Michael Griebel, Thomas Dornseifter, and Tilman Neunhoeffer, SIAM 1998.


TECHNOLOGY: Proficiency in a high-level programming language such as Fortran 90 or C is expected. Familiarity with computer algebra systems (CAS) such as Matlab, Maple, or Mathematica would be helpful.

20% Midterm exam TBD
10% Homework/Lab. assignments Selected HW/Lab. assignments to be graded
50% Programming assignments 5-6 during semester/may include presentations
20% Final exam TBD


OUTSIDE HELP: First instructor's (Dave Pruett's) office hours: TBD and by appointment. During scheduled hours, no appointment is necessary; outside of these hours, the favor of an appointment is requested.

ATTENDANCE POLICY: Individual success and the success of the course will require faithful on-time attendance.

LATE POLICY: No credit will be given for assigments turned in after the due date unless an extension period has been negotiated with the instructor at the time the assignment is made.

HONOR POLICY: Students are presumed to have high standards of integrity. To reinforce these standards, the JMU Honor Code will be strictly enforced.