Solver not showing expected order of convergence about cuibm HOT 4 CLOSED

Wrote the unit tests to calculate the order of convergence of the explicit diffusion terms. The following are observed:

• Overall order of convergence of the diffusion kernel appears to be approximately 1.5
• When only the x-derivatives for u and the y-derivatives for v are considered, the convergence is second-order. The other derivatives make use of a different kernel at the boundary, and that could be causing the unexpected order of convergence for the entire kernel.

Run the unit test to check the convergence of the explicit diffusion kernel using the following commands in the project root directory:

    make unitTests/diffusionTerm
    make testDiffusion

Proposal: Write simple 1-D codes to see how the diffusion kernel converges for different types of grids and stencils.

from cuibm.

The diffusion kernel is expected to show an order of convergence of approximately 1.5 in the L-2 norm. See the following iPython notebook for details:
http://nbviewer.ipython.org/urls/dl.dropbox.com/s/d18lm7okq4n089v/secondDerivative.ipynb?create=1

from cuibm.

Closing this for now and will revisit it later. I removed the direct forcing test cases because they were cluttering the repository, but will reintroduce them in a more organised way after further analysis.

from cuibm.

Lid-driven cavity does show second order convergence. The earlier issue was because the tolerance used was too large in magnitude (1e-5). Using 1e-8 with successive grid sizes of 20, 60, 180 and 540 gives the correct order of convergence. Use the script scripts/convergence/cavityRe100.py to check this, with the folder cases/convergence/cavityRe100/NavierStokes/20x20.

from cuibm.