Runge Kutta Discontinuous Galerkin procedure?

Ameya J · April 21, 2011, 10:30

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, 16:54

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, 04:50

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, 05:04

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, 05:34

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, 16:52

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, 06:56

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

April 21, 2011, 10:30	Runge Kutta Discontinuous Galerkin procedure?	#1
Ameya J New Member amey Join Date: Apr 2011 Posts: 7 Rep Power: 15	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...

June 9, 2011, 05:34	hi praveen	#5
Ameya J New Member amey Join Date: Apr 2011 Posts: 7 Rep Power: 15	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

July 28, 2011, 16:52	Discontinuous finite element matlab programming	#6
gmathimatikos New Member gmathimatikos Join Date: Jul 2011 Location: greece Posts: 2 Rep Power: 0	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

July 29, 2011, 06:56		#7
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	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 ssh123 likes this.

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June 8, 2011, 16:54		#2
akOOma New Member Michael Woopen Join Date: Nov 2010 Location: Aachen, Germany Posts: 12 Rep Power: 15	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

June 9, 2011, 04:50		#3
Ameya J New Member amey Join Date: Apr 2011 Posts: 7 Rep Power: 15	that means, limiters are used only in case of nonlinear equation (both Scalar and Vector) ? not in case of linear convection equation..

June 9, 2011, 05:04		#4
praveen Super Moderator Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 343 Blog Entries: 6 Rep Power: 18	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.