In 1759 Leonhard Euler published equations of motion for a fluid, applying Newton's second law, i.e., the product of mass and acceleration of a body equals the external forces acting on it. Euler's idea to express knowledge about fluid dynamics in the form of partial differential equations meant a major breakthrough. A practical shortcoming of his flow model, however, was that it did not consider friction forces. In 1845 George Stokes introduced general equations, which in the case of an incompressible fluid reduce to equations already proposed by Claude Navier in 1822. These general equations are now called Navier-Stokes equations. Understanding and controlling a large class of fluid flows was reduced to the mathematical solution of a few basic differential equations. Unfortunately, analytical solutions are very rarely available. Numerical solution of the Navier-Stokes equations has developed into a major industry, and a vital support to diverse areas of engineering, medicine and science1.
For further information see for example:
http://www.cfdreview.com/ http://www.cham.co.uk/(The latter is an Imperial College spin-out company).
This exercise is based on a CFD application called NaSt3DGP, written by Michael Griebel, Roberto Croce, Frank Koster and Michael Meyer, based on the book Griebel/Dornseifer/Neunhoefer, Numerical Simulation in Fluid Dynamics, SIAM Philadelphia (1998). The code is freely available (although not open source), and can be downloaded from
http://wissrech.iam.uni-bonn.de/research/projects/koster/NaSt3DGP/)You must abide by the licence published there. You are encouraged to visit their web site, which includes images and movies illustrating various applications of the tool.
This exercise can be done in groups of up to three, deadline Tuesday 4th March. Submit your work at the DoC Student General Office in a suitable labelled folder.
Basically, your job is to figure out how to run the computation specified in the next section as fast as you possibly can, and to write a brief report explaining how you did it.
You may find it useful to find out about:
Begin by making a copy of the files you will need:
cp -r /homes/phjk/ToyPrograms/Nast3dgp-2003 ./ cd Nast3dgp-2003 setenv NASTROOT `pwd`The final line sets the environment variable NASTROOT to the current directory path. (if you use bash you will need to adjust this final line).
Next, build the application:
cd NaSt3DGP/src/ make clean make serial cd $NASTROOTNow you can run the application. Various data files have been provided; start with a smallish one:
$NASTROOT/Scripts/RunNavcalc.sh Cavity2D-48x48x4x0.003This command should produce (after some initial data) the following output:
Step: 1 Time: 0.000000 TimeStep: 0.00208333333333 Time: 0h 0m 0.00s it: 1 res: 2.753807e+00 itmax: 200 it: 51 res: 4.851704e-02 itmax: 200 it: 101 res: 1.143685e-03 itmax: 200 it: 151 res: 1.100218e-05 itmax: 200 Iter: 200 Res: 1.63466965e-07 all It: 600 Mass Balance (rhs): -4.70586777e-16 Step: 2 Time: 0.002083 TimeStep: 0.00208333333333 Time: 0h 0m 1.00s it: 1 res: 1.907481e-02 itmax: 200 it: 51 res: 5.579380e-04 itmax: 200 it: 101 res: 3.942419e-06 itmax: 200 Iter: 138 Res: 5.59304312e-08 all It: 1014Read the script ``$NASTROOT/Scripts/RunNavcalc.sh'' to see what this did. An input file ``DataFiles/Cavity2D-32x32x4-0.003/p.nav'' describes the 3d environment in which the fluid will flow, and other details of the simulation to be run. This is pre-processed by a helper program, ``NaSt3DGP/bin/navsetup'', to produce an initial state for the mesh on which the calculation is done, which is stored in ``Junk/t.bin''. The CFD solver itself, ``NaSt3DGP/bin/navcalc'', reads this, simulates the fluid flow for a specified number of timesteps, and writes the fluid state back to ``Junk/t.bin''.
You should concentrate on the Cavity problem, which is a standard CFD test example:
http://wissrech.iam.uni-bonn.de/research/projects/koster/NaSt3DGP/apl_cavity.htmThe fluid is in a box, whose lid is sliding to one side, dragging the top surface of the fluid sideways. Interesting fluid behaviour only begins to evolve after a fairly large number of timesteps. A variety of instances of this problem have been provided, of varying size and run-time, the smallest (above) being intended for use with simulators. In practice, problems of interest can involve mesh elements or more, over hundreds of timesteps.
The second problem you might consider is more visually appealing:
./Scripts/RunNavcalc.sh FlowPastObstacle3D-51x51x13x0.4For details see
Try the following:
$NASTROOT/Scripts/RunNavcalc-cachegrind.sh Cavity2D-32x32x4-0.003This runs the application under the CacheGrind simulator, then uses the ``cg_annotate'' tool to annotate the source code. The output can be found in the file ``SourceCodeAnnotatedByCacheGrind''.
Cachegrind annotates each line of code with the following events:
Paul Kelly, Imperial College, 2003