Hello everyone. I am unsure how to implement the spatial periodicity of u and p in the convergence-order code.
The authors do not mention this spatial periodicity in their numerical experiments, though they provide a detailed explanation in another paper on the same model.
Hello,
There is nothing special about the periodicity here, you just take periodic finite element spaces for u and p. You have to care of the invariance of p by adding a constant, for example by adding \int\varepsilon pq in the variational formulation (if you use the Chorin projection method you don’t need that). The periodicity is specified by (for example for a rectangle with boundary labels 1,2,3,4 corresponding to bottom, right, top, left)
fespace Vh(Th,P2,periodic=[[1,x],[3,x],[2,y],[4,y]]);
fespace Ph(Th,P1,periodic=[[1,x],[3,x],[2,y],[4,y]]);
Here the boundary with labels 1 and 3 are identified, x being the coordinate that parametrizes the position.
The boundary with labels 2 and 4 are identified, y being the coordinate that parametrizes the position.
