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COURSE
ANNOUNCEMENT SPRING 2023
ATMS 502, CSE 566
Numerical Fluid Dynamics
13 students from 6 departments enrolled so far (Jan. 2023)
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3D view of colliding density currents
View: towards -X, +Y. Three animations shown:
- Surface velocity (vectors) and flow speed in Y-direction (shaded; blue -,
orange +);
- Two potential temperature (tan) surfaces
showing colliding density currents;
- Vertical motion
(red +, blue -) color mapped onto surface of 0.1/sec vertical vorticity
- these are the twisting toothpicks!
In English: There is +Y flow in the right half of the domain (in foreground),
-Y flow in the left. As two cold density currents move
towards the center, these characteristically different flow fields are brought together. A vortex sheet
( more) develops between
the density currents. Small perturbations grow and vorticity is stretched
( 1,
2)
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.
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FOR: This course is for those interested in
solving partial differential equations that describe
nonlinear, compressible fluid flow in 3-D settings. We utilize the high performance ACCESS
supercomputer Stampede-2. We will address
understanding of numerical methods, implementation (coding in F90 or C), and parallelization, as well as the subsequent analysis (Python)
and visualization (VisIt) of the results.
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 understanding numerical methods.
- The ability to critically evaluate numerical methods as
presented in the literature.
- 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 understanding numerical method
behavior as applied to linear and nonlinear fluid flow problems in 1-D,
2-D and ultimately 3-D settings.
- Consequence of the above: That by the end of the course you are very
comfortable with,
and capable of effectively using, supercomputer-class facilities.
- This
includes
writing and debugging code, compiling and running it, interrogating and understanding
your results, and visualizing the solution.
TOPICS: To solve fluid flow problems, you will build skills in three areas
of study: (1) fluid dynamics and kinematics; (2) programming, data
interrogation, and
visualization, and (3) the numerical methods that tie together the first two
areas. I will discuss and cover material regarding some (not all!) of
these three areas, including:
| Fluid flow |
Coding, data, visualization |
Numerical methods |
| Flow kinematics |
Languages, compilers, editors |
Multi-dimensional problems |
| Fluid flow equations |
Code optimization fundmentals |
Boundary conditions, symmetry |
| Simplifications, scaling |
Profiling, benchmarking a code |
Theory vs. practice:
Stability, accuracy |
| DNS vs. turbulence models |
Weak vs. strong parallel scaling |
Adaptive mesh refinement / nesting |
| Stability vs. shear dominance |
Visualization: idioms, tools |
Handling discontinuities |
CFD METHODS: We address and write code for finite difference and finite volume methods.
We will not cover finite element methods, for which you should consider one of the many courses in
U.I. Mechanical and
Civil/Environmental Engineering
and
Computer Science, such as:
ME 471 (Finite Element Analysis),
CEE 570 (Finite Element Methods),
CS 555 (Numerical Methods for Partial Differential Equations), and
TAM 574 (Advanced Finite Element Methods). If I've missed a relevant class here, let me know!
New this year (Spr. 2023): Compact finite differencing, WENO methods, and an introduction
to stochastic physics.
COMPUTER PROBLEMS: We wll use the
Stampede-2
supercomputer to solve fluid flow problems in one, two and three
dimensions, using regular
and nested grid approaches (we also code the nesting). I will emphasize writing clear and effective programs, as well as
(a bit of) structuring codes for efficient use of parallel computers.
Course assignments may be programmed in either of two languages used
extensively in science and engineering - Fortran 90 or C. Note that
introductory codes and plotting programs in both languages will be provided to you as a starting
point for your first computational assignment.
The behavior of the numerical solutions will be compared to known
solutions when they are available.
New this year: We will use Python extensively for data analysis & plotting solutions.
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 compressible 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.
New this year: Posting results to your (new or existing) GitHub portfolio.
PROGRAMMING EXPERIENCE: You should be comfortable with one
programming language, or
ready to learn fast! This class could be abrupt if you have no programming
experience at all. (If you have little programming
experience, contact me: Let's talk! I can help).
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 all
your programs. We will use Python for data analysis.
For those inexperienced in Fortran / C / Python / Linux, I will hold extra review sessions
early in the semester, and you can pick up the needed language(s) as you go.
New this year: IDE use to speed up your
C or Fortran coding development.
That said, we are fortunate to have outstanding departments on campus and
you might consider taking one of the many classes offered by the University's
Computer Science,
Mechanical Science & Engineering, or
Civil/Environmental Engineering departments
to strengthen your programming skills and understanding. Some of these courses are cross-listed in the
Computational Science and Engineering (CSE) program.
I also encourage consideration of courses taught
by Prof. David Bock at Parkland College
(Bock is also a Lead Visualization Programmer
at NCSA).
The goal here is using a
programming language, rather than learning one.
That said: I do go line-by-line to help students debug code. Debugging code is the #1 time
sink for this class; it is just the reality. You'll get good at it!
New this year: Using serial / parallel debuggers
to quickly find problems.
TEXTBOOK: There is no single textbook. I select materials from books
(there are many) available free as PDFs online from
the UI library; see Background, below.
INTRO: Hello! I am Brian Jewett. I teach and
carry out research in the Atmospheric Sciences Dept. My specialty is severe local storms,
and modeling of 3-D numerical modeling of a variety of atmospheric phenomena - severe
thunderstorms and squall lines, hurricanes, and snowstorms.
I am also quite interested in numerical weather prediction.
QUESTIONS? If you have any questions about the class, particularly any concerns whether your background
is sufficient to take it (answer: probably so), please feel free to contact me at the email at the top of this page. If
I don't contact you promptly, please email me again.
And remember, fluid modeling and visualization is fun!
BACKGROUND:
If you'd like to do some reading on programming, math, or statistics before or during the semester,
I recommend the following.
(Note: so-called "direct links" below work only if you are on-campus or
connected to the University network via
VPN. (You should use VPN when off-campus!)
(if you have trouble with these links, try another browser or login to UIUC or VPN - and let me know if
they still don't work.)