Grid layouts

JustPIC distinguishes vertex grids, centroid grids, and staggered velocity grids. In 2D, a staggered velocity field is supplied as:

grid_vx = xv, yc_ghosted
grid_vy = xc_ghosted, yv

The layout can be sketched as follows (• are vertices, × are centroids, u is Vx at (xv, yc) on the vertical cell faces, and v is Vy at (xc, yv) on the horizontal cell faces):

•───────v───────•───────v───────•
│               │               │
u       ×       u       ×       u
│               │               │
•───────v───────•───────v───────•

The outermost coordinate values used by interpolation are ghost images of the physical boundary values, not additional physical cells.

The diagonal coordinate of each velocity component is the vertex coordinate; the off-diagonal coordinate is the cell-center coordinate. init_particles derives particles.xvi and particles.xci from these grids and adds one ghost node on each side. Ghost nodes are nonperiodic unless periodic is set for that dimension.

using JustPIC

xv = range(0, 1, length=9)
yv = range(0, 1, length=9)
dx, dy = step(xv), step(yv)
xc = range(dx / 2, 1 - dx / 2, length=8)
yc = range(dy / 2, 1 - dy / 2, length=8)
grid_vx = xv, add_periodic_ghost_nodes(yc)
grid_vy = add_periodic_ghost_nodes(xc), yv
particles = init_particles(JustPIC.CPU, 16, 24, 8, grid_vx, grid_vy)

On a uniform range, add_periodic_ghost_nodes adds one node at each end with the grid spacing, which is also the nonperiodic ghost, so this domain is nonperiodic. On a refined coordinate vector the two differ: a periodic ghost takes the spacing of the opposite boundary cell.

The resulting layouts are:

Layout	Coordinates	Typical use
particles.xvi	vertices, ghosted	vertex fields and grid2particle!
particles.xci	centroids, ghosted	centroid fields and centroid2particle!
particles.xi_vel	staggered component grids	velocity advection

Use add_periodic_ghost_nodes for coordinate vectors that need one periodic image at either boundary. Physical-only fields can still be interpolated by disabling the relevant ghost_i or ghosted option; see the interpolation pages for complete examples.