Overview of staggered grids

In CartesianGrids, field data, such as velocity, vorticity and pressure, are stored on a staggered uniform grid. Such a grid is divided into cells, with edges (which, on a two-dimensional grid, are the same as faces) and nodes (cell centers). Nodes hold scalar-valued data. Edges, on the other hand, hold the components of vector-valued data that are normal to the respective edges; one component lies on the vertical edges, while the other is on the horizontal edges.

Furthermore, there are two different cell types: primal and dual. On the physical grid, these cell types are offset with respect to each other by half a cell spacing in each direction. In other words, the four corners of the primal (resp. dual) cell are the nodes of four dual (resp. primary) cells.

Thus, on a two-dimensional staggered grid, there are four distinct vector spaces, associated with where the data are held on the grid:

  • dual nodes,
  • dual edges,
  • primal nodes, and
  • primal edges.

In CartesianGrids, these are each distinct data types. Furthermore, the relationships between these types are defined by an underlying grid shared by all. By convention, this grid is defined by the number of dual cells NX and NY in each direction; we will often refer to it as the dual grid. For example, Nodes{Dual,NX,NY} is the type for dual node data on this grid; Edges{Primal,NX,NY} is the type for edge data on the primal cells within this same NX by NY dual grid. Note that, even though this latter type is parameterized by NX and NY, these values do not correspond to the number of primal edges in each direction on this dual grid. These values always correspond to the number of dual cells on the grid, for any data type. This makes it clear the grid is shared by all data.