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-   -   Runge Kutta Discontinuous Galerkin procedure? (http://www.cfd-online.com/Forums/main/87501-runge-kutta-discontinuous-galerkin-procedure.html)

Ameya J April 21, 2011 09:30

Runge Kutta Discontinuous Galerkin procedure?
 
Hello Friends
Can anyone explain me the detail, step by step procedure of Runge Kutta Discontinuous Galerkin Method with one example???? lets say for a simple scalar problem u_t+u_x=0
I am confused about the slope limiters, where to use it? and how they are making RK method as a TVD RK ?
It will be a great help...

akOOma June 8, 2011 15:54

Limiters are used for discontinuites. These appear in nonlinear equations (like Burgers or Euler equation). In your example u_t+u_x=0 the initial data is just convected along the x-axis with a constant velocity.

I would read the series of Cockburn and Shu introducing DG:
The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws

Ameya J June 9, 2011 03:50

that means, limiters are used only in case of nonlinear equation (both Scalar and Vector) ? not in case of linear convection equation..

praveen June 9, 2011 04:04

See the book by Hesthaven. It has matlab code also. See

http://www.nudg.org

Even linear pde might require limiters; if their data (ic and/or bc) is discontinuous, then the solution might be discontinuous.

Ameya J June 9, 2011 04:34

hi praveen
 
Hi Praveen
I have seen your location..I am also from bangalore...is it possible to meet? I have so many doubts about the DG method...if you could explain, it will be really helpful to me...
if possible, please send me your contact number at
ameya.aero@gmail.com

gmathimatikos July 28, 2011 15:52

Discontinuous finite element matlab programming
 
Hi to the CDF community
I am a mathematician and I want to start programming (dis)continuous finite elements for conservation laws. Can anyone suggest to me books or lecture notes with algorithms and examples from where i can read and understand how to program this method in matlab or fortran. How to construct the mass matrix, the stiffness matrix how to compute the normal vectors in its triangle, how to numerically calculate the integrals, affine transformation, basis functions etc.

Thanks

cfdnewbie July 29, 2011 05:56

Hello,
if you want to do DG on triangles, check out the Book by Hesthaven and Warburton.... http://www.amazon.de/Nodal-Discontin...1933269&sr=8-1

Very concise!

However, if you want to do DG on hexahedron (plus a lightning fast code), try
http://www.amazon.de/Implementing-Sp...1933333&sr=1-1

Awesome, easy, newest trend in DG...

Cheers!
cfdnewbie


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