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more explanation about grid figures

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Jan Petykiewicz 2020-01-04 18:19:49 -08:00
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15
meanas/fdmath/__init__.py
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@ -435,9 +435,15 @@ The result looks something like this:
have been omitted to make the insides of the cubes easier
to visualize.
This figure shows where all the components are located; however, it is also useful to show
what volumes those components are responsible for representing. Consider the Ex component:
two of its nearest neighbors are E fore-vectors, labeled `[E]` in the figure.
The above figure shows where all the components are located; however, it is also useful to show
what volumes those components correspond to. Consider the Ex component at `m = +1/2`: it is
shifted in the x-direction by a half-cell from the E fore-vector at `m = 0` (labeled `[E]`
in the figure). It corresponds to a volume between `m = 0` and `m = +1` (the other
dimensions are not shifted, i.e. they are still bounded by `n, p = +-1/2`). (See figure
below). Since `m` is an index and not an x-coordinate, the Ex component is not necessarily
at the center of the volume it represents, and the x-length of its volume is the derived
quantity `dx'[0] = (dx[0] + dx[1]) / 2` rather than the base `dx`.
(See also `Scalar derivatives and cell shifts`).
[figure: Ex volumes]
p=
@ -482,6 +488,9 @@ two of its nearest neighbors are E fore-vectors, labeled `[E]` in the figure.
uniform cell sizes result in off-center volumes like the
center cell here.
The next figure shows the volumes corresponding to the Hy components, which
are shifted in two dimensions (x and z) compared to the base grid.
[figure: Hy volumes]
p=
z y mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm __ +1/2 s