Staggering

The staggering of a grid function or array describes the physical placement of that grid function relative to the supporting grid structure. For example, a grid function does not have to be placed at the intersection of the ``grid lines''. It can be moved by half a grid spacing in any or all dimensions. In the latter case, it will be placed in the center of a cell.

The staggering of a grid function is a pure physical property: the values will be calculated at a different position in physical space. Still the indexing (or bookkeeping) is kept the same for all types of staggerings: the indexing of the default unstaggered grids is used.

Specifying the staggertype

The type of staggering applied to a grid function can be specified in the interface.ccl file by the attribute stagger (see Appendix E2.2). Cactus supports three kinds of staggering per dimension. The physical location of a grid function is shifted relative to the default position by adding the following values to the stagger attribute:

M

no staggering, default. Refers to the ``minus'' face relative to the default gridpoint.

C

centre staggering. The physical location is offset by half of the grid spacing in the positive direction (or to the right).

P

full staggered. P refers to plus. The physical location is offset by a full grid spacing in the positive direction (or the right).

For multi-dimensional grid functions you concatenate the code characters in 1#1 order. In Figure B4.3, we show four different staggerings of a two dimensional grid function. The solid black grid circles show the default location of the grid function at the intersections of the grid lines. In (A) we show an additional grid function of type stagger=MC: no staggering in 17#17 direction, center staggered in 20#20 direction. In (B) we have stagger=CM, and staggering each direction (stagger=CC) is shown in (C). The full staggering in (D) (stagger=PP) obeys the same rules, but is rather unusual; it is included here for completeness.

Figure: Staggered gridpoints in 2D for several staggerings. (a) : MC, (b): CM, (c): CC, (d): PP. Note that the staggering of grid functions does not change its index. The staggered gridpoints and the corresponding unstaggered points (arrows) are accessed by the same indices.

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