# fsd weighted (vn+sd) correlations

[u, v, w, y]

c = 1.0 - y
wrate = rxn_rate(c)
fsd = sqrt (sqr(ddx(c)) + sqr(ddy(c)) + sqr(ddz(c)))

sd = ((d2dx(c) + d2dy(c) + d2dz(c)) * $rod + wrate) / fsd

nx = - ddx(c) / fsd
ny = - ddy(c) / fsd
nz = - ddz(c) / fsd

vn = u * nx + v * ny + w * nz

divn = ddx(nx) + ddy(ny) + ddz(nz)

divn2 = sqr(divn)

# grad(n) : grad(n)
gradn_gradn = sqr(ddx(nx)) + sqr(ddy(ny)) + sqr(ddz(nz)) + 2*(ddx(ny)*ddy(nx)) + 2*(ddx(nz)*ddz(nx)) + 2*(ddy(nz)*ddz(ny))

absk = abs(divn)

lapc = d2dx(c) + d2dy(c) + d2dz(c)

vnsd = vn+sd

divn_nx = divn*nx

gradn_vnsd = ddx(vnsd) * nx + ddy(vnsd) * ny + ddz(vnsd) * nz

gradt_vnsd1 = ddx(vnsd) - nx * gradn_vnsd

divn2_dndn = divn2 - gradn_gradn

sign_divn2_dndn = $dsign(divn2_dndn, divn)

vnsd_divn_cor = vnsd' * divn'

vnsd_divn_nx_cor = vnsd' * divn_nx'

vnsd_divn2_dndn_cor = vnsd' * divn2_dndn'

vnsd_sign_divn2_dndn_cor = vnsd' * sign_divn2_dndn'

vnsd_divn_nx = vnsd * divn_nx

vnsd_divn2_dndn = vnsd * divn2_dndn

vnsd_sign_divn2_dndn = vnsd * sign_divn2_dndn

avg { c, u, v, w, fsd, lapc, ddx_c, ddy_c, ddz_c, d2dx_c, d2dy_c, d2dz_c }

avg fsd { u, v, w, nx, ny, nz, absk, divn, sd, gradt_vnsd1,
vnsd,
     divn_nx,
vnsd_divn_nx,
vnsd_divn_nx_cor,
     divn2_dndn,
vnsd_divn2_dndn,
vnsd_divn2_dndn_cor,
     sign_divn2_dndn,
vnsd_sign_divn2_dndn,
vnsd_sign_divn2_dndn_cor
}