# fsd weighted (vn+sd) correlations

[u, v, w, y]

c (latex="c") = 1.0 - y

fsd (latex="\Sigma_f'") = sqrt (sqr(ddx(c)) + sqr(ddy(c)) + sqr(ddz(c)))

nx(latex="n_x") = - ddx(c) / fsd
ny(latex="n_y") = - ddy(c) / fsd
nz(latex="n_z") = - ddz(c) / fsd

divn(latex="\nabla \cdot \vec{n}") = ddx(nx) + ddy(ny) + ddz(nz)

divn_sign = $dsign(1, divn)
pdivn_mask =   $positive(divn_sign)
ndivn_mask = - $negative(divn_sign)

fplus (latex="\Sigma_f^+'") = pdivn_mask * fsd
fminus(latex="\Sigma_f^-'") = ndivn_mask * fsd

avg { c, u, v, w, fsd, fplus, fminus, ddx_c, ddy_c, ddz_c }

avg fsd { u, v, w, nx, ny, nz, divn }

avg fplus { divn }

avg fminus { divn }