[dune-pdelab] Finite Volume Method with slope reconstruction

[Gregor Corbin]

Hi Marian,

this limiter function looks promising. However, it does not seem to work 
for systems of equations out of the box.

In my case, I need to generalize this to a power grid function space, 
but I struggle with the interface.

Especially it is not clear to me how  the lines

             lfs.bind(*it);
             lfs_cache.update();
             std::vector<RangeFieldType> xl(lfs.size());
             x_view.bind(lfs_cache);
             x_view.read(xl);
             x_view.unbind();

that read the local components of the solution vector would look for a 
power grid function space.

Would I have to call lfs.child(k).bind(*it) for each component? What 
does lfs_cache do? Do I need a separate cache for each child of lfs?

Cheers,

Gregor


On 02.05.2017 10:20, Marian Piatkowski wrote:
> Hi Gregor
>
>
> On 04/28/2017 03:13 PM, Gregor Corbin wrote:
>> Hello dear Dune developers,
>>
>> I have a dune-pdelab code that implements a first-order finite volume 
>> method for a hyperbolic system. Currently I am trying to implement a 
>> slope reconstruction to achieve second order accuracy in space. 
>> Therefore, before each stage of the time-stepping scheme, I need to 
>> iterate over the grid and compute the slopes on each cell.
>> My current approach is to write a limiter class and give it to the 
>> explicit one step method like this:
>>
>> oneStepMethod.apply(t,dt,x_old,x_new,LinearReconstruction);
>
> That's how it is exactly done in one of our Dune modules for the 
> lecture, dune-funcep.
> Maybe you could have a look at the code in our Git repository
> - https://parcomp-git.iwr.uni-heidelberg.de/Teaching/dune-funcep
> especially the file
> - 
> https://parcomp-git.iwr.uni-heidelberg.de/Teaching/dune-funcep/blob/master/src/common/limiter.hh
>
> I think the second class in this file is just what you are looking for.
>
> Regards,
>
> Marian
>
>>
>> In the prestage method of this class, which gets only the solution 
>> vector, i iterate over all the cells on the grid. For each cell I 
>> want to extract the solution on that cell and on it's neighbors.
>> But I have no idea how to do this.
>>
>> I appreciate any help on this problem. Is there maybe even a better 
>> way to implement slope limiting in pdelab?
>>
>> Cheers and thanks in advance,
>> Gregor Corbin
>>
>> Below is a sketch for the code of the limiter class:
>>
>> template <typename GridView, typename GFS, int n_components>
>> class LinearReconstruction
>> {
>>   enum {dim = GridView::dimension};
>>   enum {n_comp = n_components};
>>
>> public:
>>   LinearReconstruction(const GridView &grid_view, const GFS &gfs):
>>   grid_view_(grid_view),
>>   gfs_(gfs),
>>   mapper_(grid_view_),
>>   slopes_(mapper_.size(),0.0)
>>   {}
>>
>>   template<typename X>
>>   void prestage(X& x)
>>   {
>>     // reconstruct slopes
>>     for (const auto& cell : elements(grid_view_) )
>>     {
>>        // I would like to do something like in the local operator 
>> methods,
>>        // but how do I get the lfsu_s ???
>>        // is there a method to get it from the cell and the grid 
>> function space?
>>
>>        // lfsu_s = gfs_.localFunctionSpace(cell); <- does something 
>> similar exist?
>>       Dune::FieldVector<double,n_comp> u_s(0.0);
>>       for (int k = 0; k < n_comp; ++k)
>>         u_s[k] = x(lfsu_s.child(k),0);
>>
>>       // get the solutions from all the neighbors
>>       std::vector<Dune::FieldVector<double,n_comp> > 
>> u_n(pow(2,dim),0.0); // only valid for structured cubic grids
>>       int i = 0;
>>       for (const auto& is : intersections(grid_view_,cell))
>>       {
>>         const auto &neighbor = is.outside();
>>          // lfsu_n = gfs_.localFunctionSpace(neighbor); <- does 
>> something similar exist?
>>
>>          for (int k = 0; k < n_comp; ++k)
>>               u_n.at(i)[k] = x(lfsu_n.child(k),0);
>>          ++i;
>>       }
>>
>>       // use the info to reconstruct slopes
>>       slopes_.at(mapper_.index(cell)) =  // some function(u_s, u_n)
>>     }
>>   }
>>
>>   template<typename V>
>>   void poststage(V& v)
>>   {}
>> private:
>>   const GridView &grid_view_;
>>    const GFS &gfs_;
>>   using Mapper =
>> Dune::MultipleCodimMultipleGeomTypeMapper<GridView,Dune::MCMGElementLayout>; 
>>
>>   const Mapper mapper_;
>>   std::vector<Dune::FieldMatrix<double,n_comp,dim> > slopes_;
>> };
>>
>>
>>
>>
>>
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>
>
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