The term Variable stands for a physical quantity (pressure, density, etc.) or a geometric quantity (distance, coordinate, etc.) or any other quantity. A variable is always scalar in antares, except in few particular cases. As examples, mesh coordinates are stored separately in three vectors, and not in a matrix. Also, primitive CFD variables are stored separately in vectors, and not in a matrix.

Variables are stored in Instant instances as scalar multi-dimensional numpy arrays.

Even if a variable is a scalar variable, so it has only one mathematical dimension, the values of the variable may be assigned to a specific topology, therefore a multi-dimensional array.

For structured grids, an array may have more than one topological dimension, say N. Then, the shape of the array is the tuple of array dimensions. Indeed, a structured grid can be represented as a topologically regular array of points. Each point or element in this N-cube topology can be addressed with N independent indices. As an example, for a two dimensional structured grid, the number of topological dimensions is two, the topology is a square, and there are two indices i and j.

To browse the values of a one-dimensional topological array, there is no ambiguity since there is only one index. But, for a multi-dimensional topological array, the dimensions can be accessed in different ways.

With antares, the point order increases the fastest as one moves from the last to the first dimension. Applied to the above example, the point order increases in j fastest, then i.