Coordinates

Parthenon currently provides three coordinates classes ``UniformCartesian``, ``UniformCylindrical``, and ``UniformSpherical``. With small extensions, Parthenon could support other coordinate systems defined in downstream codes. Alternatively, coordinate systems can be incorporated in the fluid equations such as is done inPhoebus.

Coordinates are selected at compile time by passing the appropriate option to cmake. The default coordinate system is UniformCartesian. To select an alternative, or just to explicitly select the default, pass -DPARTHENON_COORDINATES=OPTION where OPTION is one of {UniformCartesian, UniformCylindrical, UniformSpherical}.

Coordinate objects under the Coordinates_t type are created for each meshblock. Coordinate information such as positions of different elements within each cell (cell centers, face centers, edge centers, and nodes), distance between elements, and integration elements (cell widths, edge centers, face areas, and cell volumes) can be accessed from the coordinate object for each meshblock. The coordinates object for meshblock b in a SparsePack var_pack can be accessed via var_pack.GetCoordinates(b).

Coordinate objects provide the following API:

Function	Description
`Real Dx<dir>()` `Real Dx(int dir)`	Coordinate spacing between grid lines
`Real Dxc<dir>(int idx)` `Real Dxc<dir>(int k, int j, int i)` `Real Dxc(int dir, int k, int j, int i)`	Spacing between volume centroids
`Real Dxf<dir>(int idx)` `Real Dxf<dir>(int k, int j, int i)`	Spacing between faces
`Real Xc<dir>(int idx)` `Real Xc<dir>(int k, int j, int i)`	Volume centroid position
`Real Xf<dir, face>(int idx)` `Real Xf<dir, face>(int k, int j, int i)` `Real Xf<dir>(int k,int j,int i) = Xf<dir,dir>(k,j,i)`	Face centroid position
`Real X<dir, TopologicalElement>(int idx)` `Real X<dir, TopologicalElement>(int k, int j, int i)`	Position associated with TopologicalElement
`Real Scale<dir, TopologicalElement>(int k, int j, int i)` `Real Scale<TopologicalElement>(int dir, int k, int j, int i)`	Scale factor
`Real CellWidth<dir>(int k, int j, int i)` `Real CellWidth(int dir, int k, int j, int i)`	Physical width of cell
`Real EdgeLength<dir>(int k, int j, int i)` `Real EdgeLength(int dir, int k, int j, int i)`	Physical length of edge
`Real FaceArea<dir>(int k, int j, int i)` `Real FaceArea(int dir, int k, int j, int i)`	Area of face
`Real CellVolume(int k, int j, int i)`	Volume of cell
`Real Volume<TopologicalElement>(int k, int j, int i)` `Real Volume(CellLevel cl, TopologicalElement el, int k, int j, int i)`	Generalized volume
`std::array<Real, 3> GetXmin()`	Minimum coordinates of block, including ghost cells
`std::array<int, 3> GetStartIndex()`	Number of ghost cells

Here, dir and face specify a direction and should be X1DIR, X2DIR, or X3DIR. TopologicalElement is an enum class with elements CC, F1, F2, F3, E1, E2, E3, NN, corresponding to cells, faces, edges, and nodes, with appropriate numbers to indicate directions. For Parthenon’s restricted set of supported coordinate systems, functions that take a single integer index idx are understood to correspond with the appropriate dimension’s index, i.e. idx -> i for dir = X1DIR, idx -> j for dir = X2DIR, and idx -> k for dir = X3DIR.