CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Oscillatory solution with DG scheme

Register Blogs Community New Posts Updated Threads Search

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   January 27, 2017, 15:17
Post Oscillatory solution with DG scheme
  #1
New Member
 
Adrian
Join Date: Oct 2016
Posts: 12
Rep Power: 10
AdrianN is on a distinguished road
Dear all,

I have implemented a DG-ADER scheme for the resolution of linear systems of hyperbolic conservation laws, eg. the linearized Euler equations for aeroacustics. I am trying to figure out why the scheme becomes oscillatory for a gaussian initial condition when using quadrilateral unstructured grid while it is completely non-oscillatory when using structured meshes where the cell have a random quadrilateral shape.

Please find attached three snapshots of three different solutions after several time steps: a) using a regular square grid where two columns have different width, b) using a structured trapezoidal grid and c) using an unstructured grid. As mentioned before, it can be observed that oscillations appear for case c).

The CFL has been reduced to obtain a time step much lower than the bounding value, which depends on the cell size, dimensions of the problem and degree of the polynomials. The degree of the polynomials is 2.

If someone could give me any explanation for this, it would be very helpful.
Attached Images
File Type: jpg a1.jpg (119.6 KB, 17 views)
File Type: jpg b1.jpg (162.3 KB, 17 views)
File Type: jpg c1.jpg (150.8 KB, 18 views)
__________________
Adrián
AdrianN is offline   Reply With Quote

Old   January 27, 2017, 16:51
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
why do you plot the constant-cell value instead of isolines?

however, could you plot the initial condition and the solution after a single time step on the unstructured grid? I suppose you have both pressure and velocity as well as you can superimpose also the analytical solution
FMDenaro is offline   Reply With Quote

Old   January 27, 2017, 21:02
Smile
  #3
New Member
 
Adrian
Join Date: Oct 2016
Posts: 12
Rep Power: 10
AdrianN is on a distinguished road
Thanks for your quick answer. I plot cell averaged values because I still have to figure out how to represent discontinouous arbitrary polynomial surfaces inside each cell with Paraview.

Here you can find the results for the unstructured grid after only one time step, for both the pressure and the velocity in x. I do not include the velocity in y as it exhibits the same behavior. You can also find the plots of the reference solution, represented with the color scale range of the numerical solution.

Those spurious oscillations in the velocity do not appear when using any kind of structured mesh but always appear for unstructured meshes like this one.

I don't know if I have any bug in the code that is generating such oscillations, but I believe that if so, even in the structured mesh with trapezoidal elements the problem would be noticeable, as the jacobians for the coordinate transformations are not trivial.


Kind regards,
Attached Images
File Type: jpg 1timstep_p.jpg (15.6 KB, 15 views)
File Type: jpg 1timstep_p2.jpg (11.6 KB, 14 views)
File Type: jpg 1timstep.jpg (99.8 KB, 15 views)
File Type: jpg 1timstep2.jpg (11.3 KB, 15 views)
__________________
Adrián
AdrianN is offline   Reply With Quote

Old   January 28, 2017, 04:18
Default
  #4
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
What is strange is that the velocity field has no negative values...in an oscillating solution, the first appearence is the production of spurious minimum...
however the pressure field appears with spurious modes...
FMDenaro is offline   Reply With Quote

Old   January 28, 2017, 04:46
Default
  #5
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Anyway, you need to plot exactly the values in the nodes as they are produced by the code. The constant cell-averaged value can produce a wrong analysis. For this reason I suggested to plot the initial condition to exclude that graphics produces a strange pattern also a t=0
FMDenaro is offline   Reply With Quote

Old   January 29, 2017, 15:24
Default
  #6
New Member
 
Adrian
Join Date: Oct 2016
Posts: 12
Rep Power: 10
AdrianN is on a distinguished road
Thanks for the comments. I will try to figure out how to plot all data provided by the DG solution to see if this helps. Anyway, I have checked that the solution at t=0, represented as cell averages, matches the exact solution.
__________________
Adrián
AdrianN is offline   Reply With Quote

Old   January 29, 2017, 15:36
Default
  #7
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
I suppose that the code does not distinguish between stractured or unstructured data, isn't it? Therefore also the structured grid is treated as unstructured?
Again, it is strange such a pressure pattern after a single time-step...
FMDenaro is offline   Reply With Quote

Old   February 3, 2017, 12:47
Default
  #8
New Member
 
Adrian
Join Date: Oct 2016
Posts: 12
Rep Power: 10
AdrianN is on a distinguished road
Sorry for the delay, I have been out. As you mention, it does not distinguish between structured and unstructured grid, it treats both cases identically and there are no switching options for one and other.

Could it be caused by the fact of not using any limiting techniques in the DG reconstruction, as it is usually done for the majority of hyperbolic problems? I have not implemented such techniques as the problems I am interested in consist of smooth solution without lost of regularity.
__________________
Adrián
AdrianN is offline   Reply With Quote

Old   February 3, 2017, 12:59
Default
  #9
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AdrianN View Post
Sorry for the delay, I have been out. As you mention, it does not distinguish between structured and unstructured grid, it treats both cases identically and there are no switching options for one and other.

Could it be caused by the fact of not using any limiting techniques in the DG reconstruction, as it is usually done for the majority of hyperbolic problems? I have not implemented such techniques as the problems I am interested in consist of smooth solution without lost of regularity.

A non-monotone scheme generates wiggles but that happens on both structured and unstructured grids...As I wrote, the velocity plot should show spurious minima in the solution...
FMDenaro is offline   Reply With Quote

Old   February 3, 2017, 13:01
Default
  #10
New Member
 
Adrian
Join Date: Oct 2016
Posts: 12
Rep Power: 10
AdrianN is on a distinguished road
Thanks for your help, i will have go through the code in detail again to look for errors...
__________________
Adrián
AdrianN is offline   Reply With Quote

Reply

Tags
acoustics, ader, discontinous galerkin, wave


Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
2way FSi, Initialize with steady solution, Fluent, Transient Sturcural, System Coupli mmkkeshavarzi FLUENT 1 June 28, 2024 08:03
Convergence Centurion2011 FLUENT 48 June 15, 2022 00:29
When to use upwind or central differencing schemes? quarkz Main CFD Forum 6 August 19, 2011 04:24
Question about meshing / solution scheme of CFX Coriolius CFX 8 August 1, 2004 19:39
Wall functions Abhijit Tilak Main CFD Forum 6 February 5, 1999 02:16


All times are GMT -4. The time now is 17:25.