Conversion coarse mesh to fine mesh
 

Hello,

I want to convert a coarse mesh to a fine mesh by making interpolation for the unstructred mesh. How can I do that?

Thanks in advance.

What you want needs two parts: building the finer mesh from the coarse one and interpolating the coarse solution on the finer mesh.

Now, I suspect that you may have a software that does that and you only need to know which buttons will do it (in this case the manual is typically your friend).
Is that the case or you want to know how this is done algorithmically? In the latter case the method (FV, FEM, etc) used will make the difference

Thanks for your reply.

I am using fvm and I want to know how to do that algorithmically.

My main questions are:

- How to build the finer mesh from the coarse

- Which method is used for the interpolation and how to do that?

I am looking for the answer that if the mesh is converted the fine from the coarse, how the solution is changed.

The mesh part, which, however, is not specifically tied to the FV, is not really my area of expertise. So I haven't an answer for a general polyhedral cell. But, for tetra and hexa cells you simply put a point in the barycenter of the cell and build 4 tetra or 8 hexa out of the old cell. The same also works in 2D for tri and quad cells (with 3 and 4 new cells, respectively). For general polyhedra or 2D polygons you can always split them in tetra or 2D triangles, but I'm not sure that's the correct way to proceed as that will change the nature of the cell.

Of course, once you have the new cells, you have to update the connectivity of the original grid. For tetra/tri, the method I mentioned leads to a relatively easy update because you basically just change the indices of a face adjacent cells with the new ones. Other cases might need a more dedicated approach.

Obviously, most of the details on this part really depends from your data structure. In theory, for example, you could rebuild the grid from scratch instead of updating it, but it might only make sense if the number of cells is above a certain threshold which is very case dependent.

Now, the interpolation part is what makes the FV peculiar because, in this case, you have a 1 to 1 mapping between new grid cells and old grid ones, and there is no doubt that the only meaningful interpolation is to transfer, for each coarse cell, the old value to all the new derived fine cells (on a cell by cell basis)

I think you will use the refined grid to re-run the code in order to find a new refined solution, thus the interpolation has only the goal to provide your new initial condition. This way, you can use an interpolation having as same accuracy order as your FVM.
There are several choices to refine a triangular grid, you should read the specific literature