slope limiter of discontinuous galerkin
 

Hello,friends! I'm a newcomer. I'm using discontinuous galerkin to compute shallow water equations. Because of the nonphysical oscillation I use a slope limiter. But I don't know how to use the limiter in the triangular cells around the boundary. I would appreciate any advice. Thanks!

If you solve the 2d equations you have only quadrilateral and triangle elements. For both two type of elements cockburn & Shu have been developed in their papers (multidimensional case) a methodology for slope limiting. At quadrilaterals is more straightforward while at the triangles is not.

Mainly, the limiting procedure applied when in solution domain exist discontinuities (shocks,contacts..) which created very large oscillations and large slopes. If you have discontinuities (such as by initial solution or other) then you must apply limiting procedure.If not, maybe, will be better to use a artificial viscosity because the limiting reduce the accuracy at most first order regardless if you use high order basis.

If you want give me your skype name or msn so that talk about it with more details. The limiting procedure has more aspects and is very complicate.

Thank you, Panou! Here is the thing: I know the slope limiter you mentioned. You know the implementation of slope limiter on one cell needs the cell-averaged values of its three neighboring cells. It is obviously ok when the cell is a inner cell but if the cell is a boundary cell there lacks one cell. Although DGM uses ghost-cell method to compute the numerical flux around the boundary, I can't find out some preferences on how to apply the limiters to the boundary cells. I want to get some guidance about the question above. Thanks again!

In addition, I use a slope limiter mentioned in "New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes".

Look. At boundaries cells you can take zero of average differences and thus to operate the ghost element. With other words, you can take the mean of ghost equal to mean of boundary cell.
There is not problem with this.

if you want give me a name for skype to talk here.

Thank friends. my msn is shallowwaterlake@hotmail.com and it is just registered.
Skype: zqb2011

Friends from the U.S.? MSN and SKYPE may be used widespreadly but I am from China and I am not familiar with those tools.:p

Hi,Friends, are there any group of Skype?:)