[Dune] DUNE advection w/ periodic BC w/ RK4 ?

[René Heß]

Hi,

if you are looking for examples of PDELab code with periodic boundary
conditions, we have tests that use the concept Peter described
below. You can find them here:

dune-pdelab/dune/pdelab/test/testpoisson-peoriodic.hh
dune-pdelab/dune/pdelab/test/testheat-instationary-periodic.hh

The heat equation test uses periodic boundary conditions in both
directions on a 2D grid. The poisson equation tests cover 2d and 3d.

Note: The parallel setting means that these tests must be run in
parallel with an overlapping grid, so you should call them like this:

mpirun -np 4 testheat-instationary-periodic

Note: I didn't use periodic boundary conditions for quite some time but
I know that I ran a (slightly more complicated) Stokes problem some time
ago and could reproduce the known analytical solution.


Best regards,
René

Peter Bastian <Peter.Bastian at iwr.uni-heidelberg.de> writes:

> Dear Theresa,
>
> The standard explicit RK4 method is implemented in the class
> RK4Parameter
> <https://www.dune-project.org/doxygen/pdelab/master/classDune_1_1PDELab_1_1RK4Parameter.html>
>
> in PDELab (it merely contains
> the entries of the Butcher Tableau, so you could easily add other
> methods as well).
> Sorry for answering this here, as it is actually the dune list and not a
> pdelab list.
>
> Periodic boundary conditions on YaspGrid need to be implemented "in a
> parallel setting",
> i.e. halo cells are added in the periodic directions and a communication
> steps transports
> the solution from boundary to boundary. But I did not try this for a
> long time ...
>
> Which disretization scheme did you intend to use?
>
> Best regards,
>
> Peter
>
> Am 04.12.20 um 16:11 schrieb Theresa Pollinger:
>>
>> Dear DUNE developers,
>>
>> as you may know, we are using DUNE to run FEM with the sparse grid
>> combination technique, via coupling to our code DisCoTec [0].
>>
>> Now for another project, we were simulating a pure advection problem
>> with another FEM code, which returned rather unexpected results. Now I
>> wanted to turn the exact same advection problem into a DUNE problem to
>> validate the results, but it turns out that this is quite hard. Two
>> things I am struggling with:
>>
>> - how do you set periodic boundary conditions in all directions? So
>> far I only found this old answer [1], and a test using YaspGrid looks
>> very much like periodicity is only set in one dimension, even if I
>> supply an all-true argument `periodic`.
>>
>> - What is the proper way to use a Runge-Kutta 4th-order scheme in
>> DUNE? AFAICT, pdelab only implements up to order 3 RK methods [2]?
>>
>> Maybe you could let me know if there are people who have already
>> implemented those things.
>>
>> Best,
>>
>> Theresa
>>
>>
>> [0] https://github.com/SGpp/DisCoTec
>>
>> [1]
>> https://lists.dune-project.org/pipermail/dune-pdelab/2011-October/000212.html
>> <https://lists.dune-project.org/pipermail/dune-pdelab/2011-October/000212.html>
>>
>> [2]
>> https://github.com/dune-project/dune-pdelab/blob/master/dune/pdelab/instationary/onestepparameter.hh
>>
>> -- 
>>
>> Theresa Pollinger
>>
>> Universität Stuttgart
>> Institut für Parallele und Verteilte Systeme
>> Simulation Software Engineering
>>
>> Universitätsstr. 38
>> 70569 Stuttgart
>>
>> Phone: +49 711 685 60921
>>
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>
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