Some thoughts: extra credit
OpenMP
Atms 502 Numerical Fluid Dynamics
Thu., Dec. 07, 2006
Don't use automatic parallelization! Introduce your own OpenMP directives
It's easy to do the
basic steps.
!$OMP PARALLEL DO PRIVATE (i,j,k) do k = 2,nz-1 do j =
Atms 502 Numerical Fluid Dynamics
Thu., Oct. 26, 2006
Nondimensional numbers and scaling
Nondimensional numbers
Richardson number
Nondimensional numbers
Reynolds number
Ratio of nonlinear terms to friction
Ratio of thermal/mechanical KE Ratio of stat
PD E O rder
A tm s 502 CS 505 CSE 566 N u m e r ic a l F l u id D y n a m ic s
Tue., 29 August 2006
The order of a PDE is that of the
highest-order partial derivative
"# "# = $c "t "x
We will typically look at problems that
are first-order in time.
!
9
Aug. 24, 2006
A T MS 5 0 2 - C S 5 0 5 - C S E 5 6 6
Jew ett
Outline for todays class:
1. Introduction 2. goals of this class syllabus; discussion of class structure, grading homework and computer problems connecting to NCSA
Research approaches - examples
Dec. 6, 2006
ATMS 502 - CS 505 - CSE 566
Jewett
Extra Credit: Computer Problem 6 3D nonlinear quasi-compressible flow
Due: Wednesday, Dec. 12 Description: This problem is a direct extension of problem 5 to three dimensions. A. Equations There are now five
Oct. 24, 2006
ATMS 502 - CS 505 - CSE 566
Jewett
Hints: Computer Problem 4
To make things simple, read in the type of problem (rotational/deformational case), the cone radius and origin, and the time step and plot interval. As with computer problem 3, it
Aug. 24, 2006
ATMS 502 - CS 505 - CSE 566
Jewett
Int rod uct ion a nd syllab us
Welcome to ATMS 502. Here is some key information about the course to get us started.
Contact Information
Dr. Brian Jewett - Research scientist and instructor, UIUC Atmospher
Thu. Sep. 7, 2006
ATMS 502
Jewett
Homework #1 due in class Thursday, Sep. 21, 2006 As noted in class, you may work with others on this assignment, but what you hand in must be your own work. No copying allowed! 1. Characterize the Lotka-Volterra solutions
Diffusion
We considered several approaches.
Atms 502 Numerical Fluid Dynamics
Thu., Nov. 17, 2006
Add
up terms, as in computer pgm #5, e.g. u3=u1+(advection)+(diffusion)+. tendencies (contribution) from each, and add, to get A(n+1) one process separatel
van Leer: Concepts
Concepts:
Atms 502 / CS 505 / CSE 566 Numerical Fluid Dynamics
Tue., Nov. 7, 2006
Grid zones
Not just point values Local functions describe behavior in zone If look only at zone mean: piecewise constant Next step: piecewise linear
Th
Oct. 3, 2006
ATMS 502 - CS 505 - CSE 566
Jewett
Exam 1 review
Following is a partial list of what could be on the exam. 1. Given a numerical scheme, derive the a. Amplification factor and stability condition b. Truncation error, order of accuracy; consist
Aug. 24, 2006
ATMS 502 - CS 505 - CSE 566
Jewett
Int rod uct ion a nd syllab us
Welcome to ATMS 502. Here is some key information about the course to get us started.
Contact Information
Dr. Brian Jewett - Research scientist and instructor, UIUC Atmospher
Aug. 29, 2006
ATMS 502 - CS 505 - CSE 566
Jewett
Computer program 1 - ATMS 502 - Demo code (FORTRAN first, C code begins on page 3) c c c . Set and plot the initial condition c ATMS 502 Fall, 2006 Program 1 c c Linear and nonlinear advection call ic(u1,dx
Aug. 24, 2006
ATMS 502 - CS 505 - CSE 566
Jewett
Class Survey
TERMS Boussinesq Anelastic Advection Diffusion Never heard of it Sounds familiar I think it means _ Never heard of it Sounds familiar I think it means _ Never heard of it Sounds familiar I thin
A tm s 5 0 2 N u m e r ic a l F lu id D y n a m ic s
Tue., Oct. 31, 2006
D iffu s io n
R e f: D u r r a n C h a p . 2 , 3 , A n d e r s o n e t a l C h a p 4 ; H a ltin e r & W illia m s
D iffu s io n
N o w s ta r t to c o n s id e r m u ltip le p r o c
Two dimensions - stability
Advection equation now looks like:
Atms 502 Numerical Fluid Dynamics
Thu., Oct. 19, 2006
!
" t + u(x, y)" x + v(x, y)" y = 0
To determine stability, assume
Let max u(x,y)=U, max v(x,y)=V This is called local stability
that co
Multistage methods (1)
Earlier schemes were single-stage
Atms 502 Numerical Fluid Dynamics
Tue., Oct. 17, 2006
The terms on the right side - the spatial
derivatives - were evaluated once Thus 2-time-level and 3-time-level schemes can be single-stage
Mu
Test case Atms 502 Numerical Fluid Dynamics
Thu., Oct. 12, 2006
Cone Upstream method Refinement: 3x
True Feedback No feedback
10/18/06
Atms 502 - Fall 2006 - Jewett
2
Test case
Square / top hat Lax-Wendroff Refinement: 3x
Looks a bit ugly Error 50% less
Why are we nesting
To minimize errors -
Atms 502 Numerical Fluid Dynamics
Thu., Sep. 28, 2006
Amplitude Phase speed Group velocity Truncation error
To better resolve small-scale features
which are damped out if represented by too few
grid points (e.g
Computer problem 2
Plotting
Atms 502 Numerical Fluid Dynamics
Thu., Sep. 21, 2006
Routine doplot2 is available from the class web page;
- it will overlay the true and numerical fields also Fortran.
It is available in C and
You will need to save
the in
Polar plots
Atms 502 CS 505 CSE 566 Numerical Fluid Dynamics
Tue., 12 September 2006
Key things to remember: The curves are a function of two things:
Courant number Wavenumber (really: kx = )
When you look at these plots: First identify the unit circle
Stability
Atms 502 CS 505 CSE 566 Numerical Fluid Dynamics
Tue., 5 September 2006
Consider any solution as Fourier series Examine behavior of one component
if every Fourier component is stable i.e. every possible waves amplitude is bounded then our schem