[petsc-users] Regarding Mapping

Tue Jul 14 05:19:02 CDT 2020

On Tue, Jul 14, 2020 at 5:47 AM MUKKUND SUNJII <mukkundsunjii at gmail.com>
wrote:

> Greetings,
>
> This message is again in relation to the previous series of exchanges I
> had with the PETSc development team and professors.
>
> To not be repetitive I will provide a concise description for those
> unaware. I have built a well-balanced shallow water solver based on
> ts/tutorials/ex11.c. However, the Riemann Solver that I have written
> includes the topography terms. To be well-balanced, I have made a change in
> the Riemann Solver interface in fv.c: Before the change it computes only
> one flux vector (*flux[]). But now with my modification, it computes 2 flux
> terms (*fluxL[] and *fluxR[]) and it is assigned to the left and right
> side of the interface respectively. The exact description of the problem
> itself is mentioned in the thread below.
>
> I might have accidentally found the solution while trying to figure out
> the origin of the problem.
>
> I noticed that the solver is no longer well-balanced (when running the
> adaptive mesh refinement case) when I use -dm_refine to prescribe the
> refinement level of the initial grid. I understand now, that the ‘noise'
> all across the domain is indeed caused by the wrong mapping of the left and
> right fluxes at the interface by my modification in fv.c.
>
> However, interestingly, the solver becomes well-balanced (i.e., the
> mapping is correct again) when I use -dm_forest_initial_refinement instead.
> I have tested various cases with water completely at rest to verify the
> well-balancedness of the solver while using DM of type p4est.
>
> I thought this observation might be interesting to you as I see some of
> the AMR test cases in ex11.c use -dm_refine and some others use
> -dm_forest_initial_refinement. My knowledge on P4est and DMPlex is lacking
> to explain the discrepancy between the two. Perhaps, someone else can shine
> light on this matter.
>
> Thank you very much in advance.
>

That is a very clear description. That will really help us figure out what
is happening.

For people like me who do not really understand FV methods, can you briefly
explain why we would have 2 fluxes? The simple way I think
about things, in FV you consider the state in 2 adjacent cells and then
determine a flux between them, which can be positive or negative, but
it is the same flux when viewed from either side.

  Thanks,

     Matt

> Regards,
>
> Mukkund
>
>
> Begin forwarded message:
>
> *From: *MUKKUND SUNJII <mukkundsunjii at gmail.com>
> *Subject: **Re: [petsc-users] Regarding P4est*
> *Date: *17 June 2020 at 21:20:29 CEST
> *To: *Mark Adams <mfadams at lbl.gov>
> *Cc: *petsc-users <petsc-users at mcs.anl.gov>, Domenico Lahaye <
> D.J.P.Lahaye at tudelft.nl>
>
> Yes, precisely! I am not sure how I can replicate using the original
> version of ex11.c because it does not support bathymetry.
>
> Regardless, to demonstrate the discrepancy, I have uploaded three plots.
> The scenario is a lake at rest. Essentially, you have a varying bathymetry
> but a level water surface. If the model is well balanced, then the water
> surface height must not change. The description of the files are below
>
> 1) Bathymetry.png : It shows you the bathymetry profile (z(x)) and the
> water surface height (H = h+z(x)) at t = 0.
>
> 2) Plex.png : This is the water surface height after 1 time step (0.007055
> sec)  and the dm type is Plex. As you can see, the water surface height
> is undisturbed as expected.
>
> 3) P4est.png : This is the result after 1 time step (same final time) if I
> set the dm type as p4est. The noise is in the order of 1e-3 to be a little
> more specific. Since its not specifically at the boundaries and more or
> less spread throughout, it could indeed be noise introduced. But of course
> I could be wrong.
>
> Maybe this paints a better picture.
>
> Regards,
>
> Mukkund
>
> For your reference, the Riemann Solver is a modified version of the HLL
> solver: *A simple well-balanced and positive numerical scheme for the
> shallow-water system by **Emmanuel Audusse, Christophe Chalons, Philippe
> Ung. *
> (
> https://www.intlpress.com/site/pub/files/_fulltext/journals/cms/2015/0013/0005/CMS-2015-0013-0005-a011.pdf
> )
>
> On 17 Jun 2020, at 20:47, Mark Adams <mfadams at lbl.gov> wrote:
>
> So you get this noise with a regular grid in p4est. So the same grid as
> will Plex, and you are not getting the same results.
>
> I don't know of any difference from p4est on a non-adapted grid. Can you
> reproduce this with ex11?
>
> Matt and Toby could answer this better.
>
>
> On Wed, Jun 17, 2020 at 1:33 PM MUKKUND SUNJII <mukkundsunjii at gmail.com>
> wrote:
> Greetings,
>
> I am a master’s student working on the shallow water model of the TS
> example 'ex11.c' as part of my thesis. Therefore, I am working with
> DMForest for the implementation of adaptive grids. I have a question and an
> observation.
>
> I am trying to find relevant information about interpolation that takes
> place through the routine DMForestTransferVec. Perhaps it could be my
> inability to find it, but I am unable to locate the implementation of the
> routine
>
> (forest->transfervec)(dmIn,vecIn,dmOut,vecOut,useBCs,time).
>
> Any information on this particular routine is highly appreciated.
>
> Furthermore, I have developed a well balanced Riemann Solver that includes
> topography in the model. In the process of testing both the non-adaptive
> and adaptive version, I found that my results differed when I changed the
> type of DM. For instance, when I run a scenario in a fixed, non-adaptive
> grid  with a DM of type 'P4est', I find that the well balanced nature is
> lost due to small perturbations all across the domain. However, this does
> not occur when I use a DM of type ‘plex’. Is there a radical change in the
> routines between the two DM’s? This is not as much of a question as it is
> an observation.
>
> Thank you for all of your suggestions!
>
> Regards,
>
> Mukkund
>
>

-- 
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/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20200714/83598218/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Bathymetry.png
Type: image/png
Size: 79963 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20200714/83598218/attachment-0003.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Plex.png
Type: image/png
Size: 68539 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20200714/83598218/attachment-0004.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: p4est.png
Type: image/png
Size: 150800 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20200714/83598218/attachment-0005.png>