Flagging cells for adaptive refinement

Describe flagging and clustering algorithms in more detail.

See Specifying AMRClaw run-time parameters in setrun.py for a description of the input parameters that define how Richardson extrapolation and/or the flag2refine subroutine work.

Refinement regions

In AMRClaw and GeoClaw it is possible to specify space-time regions in which refinement to a certain level is forced or a level beyond which refinement if forbidden. These are specified through the parameter rundata.regiondata.regions in setrun.py. This is a list of lists, each of which specifies a region in the form [minlevel,maxlevel,t1,t2,x1,x2,y1,y2].

For example, suppose that amr_levels_max = 6 has been specified along with these two regions:

rundata.regiondata.regions = []
rundata.regiondata.regions.append([2, 5, 10.0, 30.0, 0.0, 0.5, 0.0, 0.5])
rundata.regiondata.regions.append([3, 4, 20.0, 40.0, 0.2, 1.0, 0.2, 1.0])

The first region specifies that from time 10 to 30 there should be at least 2 levels and at most 5 levels of refinement for points in the spatial domain 0 < x < 0.5 and 0 < y < 0.5.

The second region specifies that from time 20 to 40 there should be at least 3 level and at most 4 levels of refinement for points in the spatial domain 0.2 < x < 1.0 and 0.2 < y < 1.0.

Note that these regions overlap in both space and time, and in regions of overlap the maximum of the minlevel and also the maximum of the maxlevel parameters applies. So in the above example, from time 20 to 30 there will be at least 3 levels and at most 5 levels in the region of overlap, 0.2 < x < 0.5 and 0.2 < y < 0.5.

Within these regions, how many levels are chosen at each point will be determined by the error flagging criteria, i.e. as specified by Richardson extrapolation and/or the default or user-supplied routine flag2refine. The parameters for these are described in Specifying classic run-time parameters in setrun.py.

Points that are not covered by either region are not constrained by the regions. They might be refined to any level from 1 to 6 depending on the error flagging criteria.

It is easiest to explain how this works by summarizing the implementation:

The regridding algorithm from level L to L+1 loops over all grid cells at Level L and flags them or not based on the following criteria, where (xc,yc) represents the cell center and t is the current regridding time:

• Initialize the flag by applying the error flagging criteria specified by Richardson extrapolation and/or the default or user-supplied routine flag2refine to determine whether this cell should be flagged.
• Loop over all regions (if any) for which (xc,yc,t) lies in the region specified.
  • If L >= maxlevel for any such region, set flag = False for this cell and go on to the next cell.
  • If L < minlevel for every such region, set flag = True and go on to the next grid cell.