Two independent grids with interpolation every X iterations, same domain, different grid size

[QuentinMale]

Hello,

I would like to compute with two fixed grids (without AMR):

• a main grid used by PeleLMeX (grid 1 on the attached diagram);
• a secondary, coarser grid, on which I store values at the centers of the cells (grid 2 on the attached diagram), from a different solver.

Grid 2 would only be used to interpolate its values on grid 1 every X iterations (for example a species source term added to the RHS of PeleLMeX's transport equations). I might also need to bring values from PeleLMeX (running on grid 1) to grid 2. The attached diagram illustrates the two grids for a square box with periodic conditions.

Do you think that this is easily achievable with the data structure that amrex provides? Do you have any suggestions for managing this? Maybe it's already been done somewhere in the suite of Pele codes and I can base my work on that?

Thank you very much for your inputs

[baperry2]

If, as in your figure, the coarse grid is uniform and aligned with the PeleLMeX grid with an integer coarsening factor (ideally a power of 2, but any integer can probably work), this should be quite straightforward to achieve with the AMR machinery/data structures within AMReX.

1. Create a new MultiFab with the same DistributionMapping as the PeleLMeX base grid but a coarsened BoxArray (the BoxArray class has a coarsen function)
2. use amrex::average_down to coarsen data from the PeleLMeX base grid to this new coarse grid
3. use amrex::InterpFromCoarseLevel (or PeleLM::fillcoarsepatch functions) to interpolate from the coarse grid to the PeleLMeX grid

If you want to be able to have an arbitrary coarse grid (unaligned, stretched, etc), you can probably still do this using AMReX data structures, but things might get a bit more complicated and you might have to write some custom functions.

AMReX has a ton of capability for communicating data between grids in parallel simulations, but it can be complex to use and not always well documented, so continue the discussion here if is anything needs clarification.