Adaptive Mesh Refinement

Enzo’s adaptive mesh implements a version of the Berger and Colella (1989) block-structured AMR algorithm on a Cartesian mesh. In this algorithm, cells that are flagged for refinement are combined into rectangular solid “child grid” patches with cells whose spatial resolution are an integer multiple more finely resolved than their coarser “parent grids” (with the ratio of resolutions typically, but not necessarily, being 2). This method is distinct from cell-based AMR codes in that cells are aggregated into grids, and distinct from oct-tree block structured AMR in that the grids that are created can be of arbitrary size and aspect ratio (i.e., each grid dimension can differ, rather than being a cube) and can be located at arbitrary locations within the parent grid rather than in octants of the parent grid. Enzo does not implement the full Berger and Colella method - for the sake of efficiency, it is restricted in the following ways:

  • Higher-resolution child grids must be contained completely within their parent grids, rather than spanning multiple parent grids. (Parent grids of level L are, however, allowed to have multiple child grids of level L+1.)
  • The edges of child grids must align with the cell edges of parent grids (which also implicitly requires that child grids align with the edges of their parent grids).
  • All grids are aligned with the principle axes (x,y,z), and may not be arbitrarily rotated with respect to those axes.

Enzo implements time subcycling within its AMR, with every grid level L determining its own timestep and all grids at that level taking the same timestep. This timestep is restricted so that the timestep at level L may not exceed the timestep at level L-1. The Enzo method paper describes the algorithm in more detail.

The parameters controlling Enzo’s grid hierarchy can be found in Hierarchy Control Parameters.