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COURSE ANNOUNCEMENT FALL 2013
ATMS 502, CSE 566:
Numerical Fluid Dynamics |
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Right: Visualization of final course problems from recent years.
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click either animation for full-sized movie |
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Shown on left: (1) surface Y-component winds (shaded, and vectors);
(2) potential temperature surface showing colliding density currents;
(3) vertical velocity (red +, blue -) mapped onto ~0.1/sec vertical vorticity surface.
There are +Y winds (orange) in the right half of the domain, and -Y (blue) in the left.
A vortex sheet develops between colliding density currents.
Small perturbations grow and vorticity is stretched as convergence and vertical motion
concentrate near the center axis. Merging of nearby vortices results in upscale growth
to fewer, larger rotation centers before the solution decays.
On Right: Movie of last year's problem, seen with
VisIt. View is ~towards -X, of
isosurface of perturbation potential temperature, with color along the surface
representing vertical motion (scale runs -15 to +15 m/s). A cold thermal descends to the
surface ahead of a descending density current. Shear of the Y-flow component between
the density current, environment, and cold thermal leads to a rolling up of the
vortex sheet, and significant vorticity as it interacts with the isolated cold source.
(Computation, parallelization and visualization were all parts of the grade).
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FOR: This course is for those interested in numerically
solving partial differential equations that describe
compressible fluid flow,
utilizing a high performance production XSEDE supercomputer,
likely
Stampede.
KEY OBJECTIVES: that those taking the course leave it with
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- A thorough understanding of the fundamentals - the basis
for
choosing and evaluating numerical methods
- The ability to critically interpret numerical methods as
presented in the literature. We will work through several papers and
examine their descriptions of their methods and how they are assessed
in terms of stability, accuracy, and error characteristics
- Most important: the ability to apply these methods to
high-performance computers. There will be no "black boxes" (other than visualization
packages) in the
course - the emphasis is on coding and understanding numerical method
behavior as applied to linear and nonlinear fluid flow problems in 1-D,
2-D and 3-D settings.
MATERIAL COVERED: The course focuses on the use of
numerical
methods in
solving wave equations. Content is directed at understanding how
finite difference, finite volume and semi-Lagrangian methods affect the
solution of
advection and Burger's equations. Topics include time and space
approximations, use
of staggered meshes, nested grid implementation and limitations,
temporal and directional splitting, monotonicity, positive
definiteness, and flux limiting. Nonlinear systems including the
shallow-water,
Euler equations, and quasi-compressible systems are discussed.
Throughout the course,
findamental principles such as stability, accuracy, convergence,
nonlinear
instability and aliasing are introduced and are related to the behavior
of different
numerical approximations.
COMPUTER PROBLEMS: We will (likely)
use the TACC Stampede
supercomputer to solve fluid flow problems in one, two and three dimensions, using regular
and nested grid approaches.
We will emphasize writing clear and effective programs, as well as
structuring codes for efficient use of parallel computers.
Course assignments may be programmed in Fortran 90 or C, and introductory
codes and plotting programs in both languages will be provided.
The behavior of the numerical solutions will be compared to known
solutions when they are available.
The computing objectives are (a) getting everyone comfortable and
familiar with our programming environment on a production supercomputer, (b)
getting started with 1-D codes before we add complexity, and (c)
working up to 3-D nonhydrostatic nonlinear problems by the end of
class. Each class computer problem will be designed to build on the last
to make understanding and completing the assignments more
straightforward for all.
PROGRAMMING EXPERIENCE:
You should be comfortable with a programming language, or
ready to learn. This class could be abrupt if you have no programming
experience at all, as we get going fairly quickly. To help everyone get
started and to begin at a common starting point, I will pass out an
introduction (sample) program at the start of class (in Fortran 90 and
also in C) which will serve as a basis upon which you will build your
later programs.
For those rusty in F90 or C (or Linux),
there will be review sessions early in the semester.
If you feel your programming experience is not very strong and you want to do some preparation
before class starts, I recommend the following:
NEW FOR FALL 2013:
- General rearrangement of class material; introduction of topics from other textbooks
- More background on fluid flow equations, kinematics and dynamics;
- Greater emphasis on visualization and applying vis tools to your results, including
VisIt and/or Paraview;
- Writing/reading NetCDF files in C/Fortran for visualization;
- New (brief) section on numerical analysis, initialization and prediction.
TEXT:
There is no official text yet. It will be one or more of those available free from the UI library online.
INTRO: Welcome; I am Dr. Brian Jewett. I teach
and
carry out research in the Atmospheric Sciences Dept. My specialty is 3d
numerical modeling of a variety of atmospheric phenomena - severe thunderstorms and squall lines,
hurricanes, and heavy snowstorms.
If you are considering taking 502/566, read on:
- You need an understanding of calculus, some matrix algebra, and preferably exposure to PDEs.
- There will be homework assignments (for which I
encourage students to work together - but turn in your own work), and
three exams (2+final)
- We will use simple(r) ways to view our data as well as fairly sophisticated
visualization tools. You may install these on your own laptop or use classroom PCs.
- There are no black boxes in the course other than the visualization
packages; you will write the core programs and analyze the results. Do
know that I am always willing to help work out problems with coding,
and I do provide test results (for problems similar to but not
identical to the assignments) with which you can evaluate your programs.
If you have any questions about the class, please feel free to
contact me.
