Jaekwang,

DoFTools::make_hanging_node_constraints (dof_handler, constraints);
>
> DoFTools::make_periodicity_constraints(dof_handler,6,5 //Boundary ID 6 is 
> outlet and 5 is inlet 
>
>                                        ,0,
>
>                                         constraints
>
>                                         );
>
>              
>
>
> Question 1. 
>
> I assume that this does same thing as Triangulation.add_periodicity () + 
> Gridtools::collect_periodic_faces(). 
>
> Isn't it? 
>
No, in general it isn't. This identifies degrees of freedom across periodic 
boundaries by writing the corresponding constraints in a ConstraintMatrix 
(or AffineConstraints) object.
However, for discontinuous approaches you normally don't want to enforce 
continuity across periodic boundaries strongly, but in a weak sense.

Question 2. 
>
> What I don't know now is when I call 'integrate_boundary_term' function in 
> the mesh worker 
>
> how can I assess neighbor cell information?
>
> For example, when I assemble for left end cell - the influx should be 
> described by right-end cell at previous time solution solution at previous 
> time.
>
> To summary, I don't know how to call neighbor (described by periodic) cell 
> solution within the 'integrate_boundary term' function
>
If you call add_periodicity() on a Triangulation object, the periodic faces 
are treated as internal faces in MeshWorker. 
This means that you will not access them in a "integrate_boundary_term" 
function but in a "integrate_face_term" function.

Apart from that, you can always ask a cell iterator for its periodic 
neighbor on a given face via CellAccessor::periodic_neighbor() 
<https://www.dealii.org/9.0.1/doxygen/deal.II/classCellAccessor.html#a1a319df6946be1c4b522f2040d31eb46>
.

Best,
Daniel

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