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John May 23, 2008 13:30

DG introduction
 
I'm familiar with CG well (and FVM as well), but I do not have any knowledge about DG, can anyone suggest me a suitalbe an introductory reference (brief that gives concept)

Jed May 23, 2008 15:20

Re: DG introduction
 
I like the sections on DG in Karniadakis & Sherwin `Spectral/hp element methods for CFD'. For elliptic problems, there are several inequivalent approaches with different stability, consistency, and computational properties. Arnold and others 2002 `Unified analysis of DG for elliptic problems' is a good start, but somewhat technical.

jinwon park May 23, 2008 17:47

Re: DG introduction
 
B.Q. Li, 'Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer', Springer 2005

Rami May 25, 2008 09:13

Re: DG introduction
 
John,

I have received lecture notes from Bernardo Cockburn (cockburn@math.umn.edu), one of the major players in this field. You may contact him directly, or else send me your email and I'll forward it to you.

ami

John May 25, 2008 09:28

Re: DG introduction
 
please forward a copy to me (john.dongarra@gmail.com), thanks.

Rami May 25, 2008 09:45

Re: DG introduction
 
Please find it in your mailbox.

John May 25, 2008 11:27

Re: DG introduction
 
Thank, but what you sent to me is not a Lecture note, but is a review paper, which is not useful for starter!


Rami May 26, 2008 09:45

Re: DG introduction
 
Well, this is what I had from him. As a last help I can offer, have a look at this ppt presentation: www.iacmm.org.il/ISCM20/DGM_ISCM20T.ppt

Hopefully, this will be helpful.


John May 26, 2008 12:22

Re: DG introduction
 
Thanks for your knid effort.

Rami May 27, 2008 02:23

Re: DG introduction
 
You are welcome. If it does not serve your need, the cats pictures at least are cute...

SKKhan August 2, 2011 03:20

Quote:

Originally Posted by Rami
;55274
John,

I have received lecture notes from Bernardo Cockburn (cockburn@math.umn.edu), one of the major players in this field. You may contact him directly, or else send me your email and I'll forward it to you.

ami

please forward a copy to me (shahzadakhurramkhan@gmail.com), thanks. as soon as possible because I am studying the Book "Discontinuous Finite Element For Fluid Dynamics and Heat Transfer" by Ben Q.Li. I think there are typing error so give the any useful material about DFEM. I am very thankful of you.

cfdnewbie August 2, 2011 03:25

I've found the Book by Li not very good... why not try the Hesthaven book (has become standard in the field) or Kopriva's DGSEM? I find both of them to be much more readable as well---

SKKhan August 2, 2011 03:29

Quote:

Originally Posted by cfdnewbie (Post 318422)
I've found the Book by Li not very good... why not try the Hesthaven book (has become standard in the field) or Kopriva's DGSEM? I find both of them to be much more readable as well---

Book Name and Author Name DGSEM

cfdnewbie August 2, 2011 03:33

sir, yes, sir!!


http://www.amazon.com/Nodal-Disconti.../dp/0387720650

http://www.amazon.com/Implementing-S.../dp/9048122600

panou August 2, 2011 07:34

For more and advanced information on modal DG method you can look the thesis of Landamann:

http://elib.uni-stuttgart.de/opus/vo...9/pdf/diss.pdf

Also, if you want to understand very well the dg method you must read by books or papers the below matters:

1.Schemes of finite volumes theory (due to relation of dg with finite volumes (discontinuity at interfaces-fluxes))
2.Riemann solvers (mainly approximate Riemann solvers)
3.Spectral & high order Elements

SKKhan August 2, 2011 09:25

Quote:

Originally Posted by panou (Post 318482)
For more and advanced information on modal DG method you can look the thesis of Landamann:

http://elib.uni-stuttgart.de/opus/vo...9/pdf/diss.pdf

Also, if you want to understand very well the dg method you must read by books or papers the below matters:

1.Schemes of finite volumes theory (due to relation of dg with finite volumes (discontinuity at interfaces-fluxes))
2.Riemann solvers (mainly approximate Riemann solvers)
3.Spectral & high order Elements

thanks I will Study these materials about DG.

cfdnewbie August 2, 2011 12:38

Quote:

Originally Posted by panou (Post 318482)
For more and advanced information on modal DG method you can look the thesis of Landamann:

http://elib.uni-stuttgart.de/opus/vo...9/pdf/diss.pdf

Also, if you want to understand very well the dg method you must read by books or papers the below matters:

1.Schemes of finite volumes theory (due to relation of dg with finite volumes (discontinuity at interfaces-fluxes))
2.Riemann solvers (mainly approximate Riemann solvers)
3.Spectral & high order Elements

Well, in my opinion, most people nowadays tend to use nodal DG schemes, at least from what I know about some of the "big players" in the field.... but modal sure has its own advantages, so it's good to know at least the basics....
I'd still recommend DG SEM by Kopriva for a beginner...

Regarding the Riemann solvers: that depends on what you want to do with your code....
for well-resolved problems, the Riemann solvers shouldn't really matter at all, but for underresolved probs, I agree...

Cheers!

panou August 2, 2011 16:18

The choice of Riemann solver play important role for DG formulation. Is the way that an element derives information by neighbour elements.
Mainly for solutions with large gradients or discontinuities(such as shocks)
the Riemann solver is crucial part due to the resolution of solution at these regions.

cfdnewbie August 2, 2011 16:32

Quote:

Originally Posted by panou (Post 318574)
The choice of Riemann solver play important role for DG formulation. Is the way that an element derives information by neighbour elements.
Mainly for solutions with large gradients or discontinuities(such as shocks)
the Riemann solver is crucial part due to the resolution of solution at these regions.

Hello panou, I tend to half-disagree with you :))
Sure, Riemann solver couple the system, but due to the higher polynomial approximation in the cells, jumps at interfaces tend to be much smaller than for FV... Thats why you can get away with using a cheaper Riemann solver than FV. In fact, as long as you are decently resolved, lax Friedrichs is ok most of the time!

Regarding shock capturing: shocks on coarse grids are generally not captured at the grid cell interface, but within the cell!! And thats done by stabilizing with viscosity, not by the Riemann solver.


So, as you see, in DG Riemann solvers play a less important role than in FV!

Cheers!


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