[dune-pdelab] Staggered Grids?

[Bernd Flemisch]

Hi Gregor,

I can't provide a very detailed view on this, but a coarse roadmap would 
be to use a P/Q1-P0 CompositeGridFunctionSpace, P0 for u_1 and P/Q1 for 
u_2. I can't find any usage of CompositeGridFunctionSpace in the current 
PDELab tutorial, but
https://gitlab.dune-project.org/pdelab/dune-pdelab/blob/master/dune/pdelab/test/testutilities.cc
should get you there.

You should adapt and combine things from Tutorials 01 and 02 from
https://gitlab.dune-project.org/pdelab/dune-pdelab-tutorials

For the fluxes over cell-centered volumes, you would use the 
"..._skeleton" functions as in Tutorial 02, while for the 
vertex-centered volumes, you would use the "..._volume" parts as in 
Tutorial 01. For the latter, you would divide each primal element into a 
corresponding amount of subcontrol volumes. The total fluxes would be 
assembled automatically from these contributions.

Hope this helps. Kind regards
Bernd


On 01/23/2018 10:29 AM, Gregor Corbin wrote:
> Hello everyone,
>
> I need to implement a method on staggered grids and would like to know
> if it is possible in PDELab, and if so, how?
>
> More specifically, I have a system of hyperbolic equations that will be
> solved with a first-order finite volume method. It has the structure
>
>      d_t u_1 + dx F(u_2) = 0,
>
>      d_t u_2 + dx G(u_1,u_2) = 0.
>
> The solution components u are split into two parts, u_1 and u_2.
>
> u_1 is associated with some grid, let's say grid1, (a tensor product
> grid, i.e. YASP grid, in my case) as usual. But u_2 should be defined on
> the complement grid2, i.e. the grid that has the corners of grid1 as the
> new cell centers, and the cell centers of grid1 as the new cell corners.
>
> I don't think that the usual local operators can handle this situation,
> so I'm currently inclined to iterate over the grid, evaluate the
> solution from the GFS, and compute the updates manually, without the
> help of grid operators.
>
> I'd really appreciate your help.
>
> Cheers,
>
> Gregor
>
>
>
>
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-- 
_______________________________________________________________

Bernd Flemisch                         phone: +49 711 685 69162
IWS, Universität Stuttgart             fax:   +49 711 685 60430
Pfaffenwaldring 61            email: bernd at iws.uni-stuttgart.de
D-70569 Stuttgart            url: www.hydrosys.uni-stuttgart.de
_______________________________________________________________

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