ISC 5935
Spring 2015
Study plan for Wenju Zhao
Supervisor: John Burkardt
12 January 2015

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Wenju Zhao proposes the following special topic activity for his 
participation in the course.  

He has been writing a program to solve the incompressible Navier-Stokes 
equations and the Cahn-Hilliard equations in 3D, using the finite element 
method, and wishes to carry out some research activity and write papers based 
on these programs.

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STEP 1: Navier Stokes Benchmarks:
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Wenju will begin by verifying the Navier Stokes code, that is, by
setting up standard benchmark problems, solving them, and comparing
the results and timings to other published data.  

I believe he can start with the 2D Navier-Stokes equations.
Here, a source of two such problems is the paper by Oosterlee:

  1) Skewed driven cavity, parallelipiped region, (30 degrees or 45 degrees)
  2) L-shaped region

For the 3D Navier-Stokes equations, a source of problems is the paper by Ethier:

  1) Exact solution over arbitrary region, exponential functions
  2) Exact solution over arbitrary region, trigonometric functions (steady, inviscid)

or http://www.featflow.de/en/benchmarks.html:

  1) CC3D
  2) PP3D
  3) Flow around a cylinder

or http://www.cfd-online.com/Wiki/Validation_and_test_cases, where 3D cases
include

  1) Ahmed body
  2) Free-surface piercing NACA 0024 Hydrofoil

Following the benchmark calculations, Wenju will produce a report
listing relevant comparisons, including:

  1) number of elements
  2) number of time steps
  3) CPU time

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STEP 2: Cahn-Hilliard Benchmarks:
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For the Cahn-Hilliard equations, Wenju needs to identify a suitable
set of benchmark problems, and then set up and solve these problems
with his code, and produce a second report.

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STEP 3: Research
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Once the test problems have been run, further investigations can be done
to determine the conditioning of the system, conservation of energy, and
other tests.

If there is time, Wenju will produce a third report, giving the results
of these further investigations with his codes.

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Changes:
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There is a possibility that, during this project, Wenju may wish to
change the direction of his research; this is acceptable as long as
we discuss it beforehand and can agree on a corresponding modification of this 
existing agreement.

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References:

Featflow: CFD Benchmarking Project
http://www.featflow.de/en/benchmarks.html

CFD Wiki
http://www.cfd-online.com/Wiki/Validation_and_test_cases

C Ross Ethier, D A Steinman,<br>
Exact fully 3D Navier-Stokes solutions for benchmarking,<br>
International Journal for Numerical Methods in Fluids,<br>
Volume 19, Number 5, March 1994, pages 369-375.

C W Oosterlee, P Wesseling, A Segal, E Brakkee,<br>
Benchmark solutions for the incompressible Navier-Stokes equations in
general coordinates on staggered grids,<br>
International Journal for Numerical Methods in Fluids,<br>
Volume 17, 1993, pages 301-321.