[petsc-users] Linear Reconstruction of Gradients

[Matthew Knepley]

On Tue, May 12, 2020 at 4:21 AM Shashwat Tiwari <shaswat121994 at gmail.com>
wrote:

> Hi,
> I am trying to write a second order upwind finite volume scheme on
> unstructured grid using DMPlex. I am performing gradient reconstruction
> using the "DMPlexReconstructGradientsFVM" function as well as a
> "ComputeGradient" function that I have written myself, in which, I loop
> over faces and add the gradient contribution to neighboring cells of the
> face (similar to what is done in "DMPlexReconstructGradients_Internal") .
> The results don't seem correct when using the
> "DMPlexReconstructGradientsFVM" function where as when using my own
> function, the second order is achieved. To investigate, I looked at the
> gradients computed by these two functions, and noticed that
> "DMPlexReconstructGradientsFVM" assigns a zero value to the gradient of
> cells with less than three neighbors, for example, boundary cells (which I
> assume is because leastsquares requires over-constrained system of
> equations and hence, atleast three neighbors), where as, I am not
> considering this factor in my "ComputeGradient" function and adding the
> contribution to neighboring cells for all interior and partition faces.
> Other than this, both the functions seem to compute similar values for
> gradients on all the other cells and I suspect, zero values for certain
> cells might be causing the problem. I wanted to know if I am missing out on
> some crucial step in the code which would enable the
> "DMPlexReconstructGradientsFVM" function to compute gradients for cells
> with lesser number of neighbors, and also if there is a way to augment the
> leastsquares stencil, i.e. to use, say, vertex neighbors instead of face
> neighbors to reconstruct gradients. Also, kindly let me know if my analysis
> of the problem is wrong and if there might be some other issue.
>

I am sure you are right. It should be possible to do exactly as you say
in DMPlexReconstructGradientsFVM(). I must have just messed it up in the
initial implementtion. If
you want to make a simple MR, or send your patch, I can help get it
integrated.

  Thanks!

     Matt


> I am attaching my code for your reference. You can find the use of both
> "DMPlexReconstructGradientsFVM" function and "ComputeGradient" function
> (just uncomment the one you want to use) inside "ComputeResidual" function.
> I am also attaching the Gmsh file for the mesh I am using. You can run the
> code as follows:
>           mpiexec -n <NumProc> ./convect -mesh square_tri.msh
>
> Please let me know if you need anything else.
>
> Thanks and Regards,
> Shashwat
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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