The Mesh hierarchy in Athena is very flexible. For example, it allows for an arbitrary number of levels, and an arbitrary number of independent Domains at each level. However, there are some important restrictions on the geometry of levels, as described below.

The code tests whether the Mesh hierarchy violates any of these restrictions at the start of execution of each run; it should quit with a warning message if a problem is found.

Restrictions on Domains touching the boundary of the root Domain

Fine (level>0) Domains may touch the boundaries of the root (level=0) Domain (see the examples below). In such cases, the physical boundary conditions applied to the root Domain will also be applied to the finer level Domains.

However, with periodic BCs, the finer level Domains must touch both sides of the root Domain, or none at all. Thus, the first two examples above are not allowed with periodic BCs, while the third is allowed.

Space is required between Domains at different levels

The edges of Domains at different levels cannot touch, unless they also touch the boundary of the root Domain. In addition, there must be at least nghost (generally 4) cells on the finest level between the boundaries of Domains at different levels. This space is needed so that the ghost zones on the finer level can be set by a prolongation of active cells (not ghost zones) on the coarser level. The first example below is allowed (except with periodic BCs), and the following two are not allowed.

Domains at the same level cannot touch

In order to provide space for the ghost zones of each Domain to be set by prolongation, Domains at the same level cannot touch, or be closer than nghost (usually 4) cells on that Domain. If Domains touch, then in principle the ghost zones can be set by mapping them to the corresponding active cells on the neighboring Domain, however this logic is complicated with face-centered magnetic fields in MHD and has not been implemented (yet). None of the examples below are allowed.

Maximum refinement ratio between successive levels is two

The ratio of grid spacing between successive levels is always restricted to be two. Any arbitrary number of levels is allowed to reach any desired resolution, but each level in the Mesh hierarchy must involve a decrease in the size of the grids cells of two and only two.