[aspect-devel] Discrepancy in L2 Error of Velocity between deal.II and ParaView (Ying He)
Ying He
yinghe at math.ucdavis.edu
Mon Oct 24 19:35:43 PDT 2016
Hi Harsha,
On 2016-10-24 17:27, aspect-devel-request at geodynamics.org wrote:
> Send Aspect-devel mailing list submissions to
> aspect-devel at geodynamics.org
>
> To subscribe or unsubscribe via the World Wide Web, visit
> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/aspect-devel
> or, via email, send a message with subject or body 'help' to
> aspect-devel-request at geodynamics.org
>
> You can reach the person managing the list at
> aspect-devel-owner at geodynamics.org
>
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of Aspect-devel digest..."
>
>
> Today's Topics:
>
> 1. Discrepancy in L2 Error of Velocity between deal.II and
> ParaView (Harsha Lokavarapu)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 24 Oct 2016 17:22:53 -0700
> From: Harsha Lokavarapu <hlokavarapu at ucdavis.edu>
> To: aspect-devel at geodynamics.org
> Subject: [aspect-devel] Discrepancy in L2 Error of Velocity between
> deal.II and ParaView
> Message-ID:
> <CAL-NPugP=x2rKQ3B-8NmuDZUUM78t93Jhzqok84hDZpTg+LwMA at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Hi all,
>
> Elbridge Gerry Puckett and I are interested in benchmarking particle
> interpolation algorithms for a time dependent flow. However, we are
> initially verifying that the computed solution without particle
> interpolation is converging to the analytical solution.
>
> The attached equations.pdf contains the equations that we are
> interested in
> solving as well as the analytical solution we are interested in
> computing.
>
>
> When measuring the error of velocity and pressure in the L1, and L2
> norms
> between the analytical solution and the computed solution via a call to
> function VectorTools::integrate_difference
> <https://dealii.org/8.4.0/doxygen/deal.II/namespaceVectorTools.html#a01174a2a7e2ee8fa6abdfdd93ac7a317>
> (similar
> to that of the benchmarks SolKz, SolCx, and Inclusion), the computed
> errors
> are
>
> Global Refinement Level | L1 Velocity | L1 Pressure |
> L2 Velocity | L2 Pressure
> ___________________________________________________________________________________
> 2 | 1.163288e+00 |
> 6.499700e-04 | 9.156779e-01 | 1.008813e-03
> 3 | 1.164841e+00 |
> 2.445984e-04 | 9.164871e-01 | 3.097737e-04
> 4 | 1.165503e+00 |
> 7.143108e-05 | 9.168331e-01 | 8.375593e-05
> 5 | 1.165702e+00 |
> 1.914297e-05 | 9.169377e-01 | 2.168699e-05
>
Can you tell me whether the errors computed above using particle
interpolation or not?
First of all, the differences of the errors between velocity and
pressure, I think, is probably due to the Q2-Q1 finite element choices
for velocity and pressure. To compute the velocity L2 error, it needs
more Gauss quadrature points than pressure. But from your paraview
outputs for velocity errors and pressure errors, they both have large
point-wise errors near the shell boundaries at the vertices of boundary
cells compared to other vertices but definitely much smaller than the
errors computed in the table above. Did you enable the interpolation
option for paraview output. If you didn't, can you reproduce and look at
the output of velocity error again. I am suspecting the Gauss quadrature
rules for the cells with curved inner/outer boundary wasn't set up
correctly... so more quadrature points needed at the curved boundaries
more larger errors... but it may need other developers' second opinions.
> The visualisation output of the magnitude of velocity for global
> refinement
> level of 5 with velocity glyphs looks like:
>
> [image: Inline image 1]
>
> Using the builtin calculator of ParaView to compute the L2 norm of the
> error via the equation
>
> sqrt(abs(velocity_X + coordsY)^2 + abs(velocity_Y - coordsX)^2)
>
> produces the following result.
>
> [image: Inline image 2]
>
>
> Why is there this discrepancy in error between the dealii function,
> VectorTools::integrate_difference
> <https://dealii.org/8.4.0/doxygen/deal.II/namespaceVectorTools.html#a01174a2a7e2ee8fa6abdfdd93ac7a317>
> and
> the discrete L2 norm computed through Paraview? Is this at all related
> to
> the geometry of the domain?
>
> For completeness, the visualisation output of pressure with velocity
> glyphs
> looks like:
>
> [image: Inline image 3]
>
> The error of the pressure computed within ParaView for the same grid
> refinement via the equation:
>
> sqrt((p - (-1 + mag(coords)))^2)
>
> equates to:
>
> [image: Inline image 4]
>
> Truly appreciate the help!
> Thank You,
> Harsha
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL:
> <http://lists.geodynamics.org/pipermail/aspect-devel/attachments/20161024/0171379c/attachment.html>
> -------------- next part --------------
> A non-text attachment was scrubbed...
> Name: image.png
> Type: image/png
> Size: 222272 bytes
> Desc: not available
> URL:
> <http://lists.geodynamics.org/pipermail/aspect-devel/attachments/20161024/0171379c/attachment.png>
> -------------- next part --------------
> A non-text attachment was scrubbed...
> Name: image.png
> Type: image/png
> Size: 430801 bytes
> Desc: not available
> URL:
> <http://lists.geodynamics.org/pipermail/aspect-devel/attachments/20161024/0171379c/attachment-0001.png>
> -------------- next part --------------
> A non-text attachment was scrubbed...
> Name: image.png
> Type: image/png
> Size: 456364 bytes
> Desc: not available
> URL:
> <http://lists.geodynamics.org/pipermail/aspect-devel/attachments/20161024/0171379c/attachment-0002.png>
> -------------- next part --------------
> A non-text attachment was scrubbed...
> Name: image.png
> Type: image/png
> Size: 401407 bytes
> Desc: not available
> URL:
> <http://lists.geodynamics.org/pipermail/aspect-devel/attachments/20161024/0171379c/attachment-0003.png>
> -------------- next part --------------
> A non-text attachment was scrubbed...
> Name: equations.pdf
> Type: application/pdf
> Size: 74867 bytes
> Desc: not available
> URL:
> <http://lists.geodynamics.org/pipermail/aspect-devel/attachments/20161024/0171379c/attachment.pdf>
> -------------- next part --------------
> A non-text attachment was scrubbed...
> Name: to_reproduce.tar.gz
> Type: application/x-gzip
> Size: 6747 bytes
> Desc: not available
> URL:
> <http://lists.geodynamics.org/pipermail/aspect-devel/attachments/20161024/0171379c/attachment.bin>
>
> ------------------------------
>
> Subject: Digest Footer
>
> _______________________________________________
> Aspect-devel mailing list
> Aspect-devel at geodynamics.org
> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/aspect-devel
>
> ------------------------------
>
> End of Aspect-devel Digest, Vol 59, Issue 50
> ********************************************
--
Best,
Ying
More information about the Aspect-devel
mailing list