177 lines
3.5 KiB
Text
177 lines
3.5 KiB
Text
# fsd weighted (vn+sd) correlations
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[u, v, w, y]
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c(latex="c") = 1.0 - y
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wrate (latex="\dot{\omega}") = rxn_rate(c)
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f (latex="\Sigma_f'")= sqrt (sqr(ddx(c)) + sqr(ddy(c)) + sqr(ddz(c)))
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uc = u' * c'
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lapc(latex="\Delta c") = d2dx(c) + d2dy(c) + d2dz(c)
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sd(latex="S_d") = ($rod * lapc + wrate) / f
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nx(latex="n_x") = - ddx(c) / f
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ny(latex="n_y") = - ddy(c) / f
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nz(latex="n_z") = - ddz(c) / f
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nx_lvl = sqr(nx')
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ny_lvl = sqr(ny')
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nz_lvl = sqr(nz')
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nx2 = sqr(nx)
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ny2 = sqr(ny)
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nz2 = sqr(nz)
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nn = nx2 + ny2 + nz2
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unx = u * nx
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vny = v * ny
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wnz = w * nz
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unx_fluc = u' * nx'
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vny_fluc = v' * ny'
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wnz_fluc = w' * nz'
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vn(latex="v_n") = unx + vny + wnz
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divn(latex="(\nabla \cdot \mathbf{n})") = ddx(nx) + ddy(ny) + ddz(nz)
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divn2 = sqr(divn)
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# grad(n) : grad(n)
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gradn_gradn(latex="\nabla \mathbf{n} : \nabla \mathbf{n}") = sqr(ddx(nx)) + sqr(ddy(ny)) + sqr(ddz(nz)) + 2*(ddx(ny)*ddy(nx)) + 2*(ddx(nz)*ddz(nx)) + 2*(ddy(nz)*ddz(ny))
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gradn_gradn_lvl = gradn_gradn' * gradn_gradn'
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absk = abs(divn)
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divn_lvl = sqr(divn')
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absk_lvl = sqr(absk')
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unxsd = u + nx * sd
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vnsd = vn+sd
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vn_lvl = sqr(vn')
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sd_lvl = sqr(sd')
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vnsd_lvl = sqr(vnsd')
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u_lvl = sqr(u')
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v_lvl = sqr(v')
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w_lvl = sqr(w')
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vnsd_nx = vnsd * nx
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vnsd_nx_fluc = vnsd' * nx'
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vnsd_nx_lvl = sqr(vnsd_nx')
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# u * nx_lvl
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# nx * unx_fluc
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vn_nx = vn' * nx'
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sd_nx = sd' * nx'
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u_nx_nx = u' * sqr(nx')
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v_ny_nx = v' * ny' * nx'
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w_nz_nx = w' * nz' * nx'
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vnsd_divn = vnsd * divn
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vnsd_divn_fluc = vnsd' * divn'
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nx_divn = nx' * divn'
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u_divn = u' * divn'
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v_n_divn (latex="\mathbf{v}'' \cdot \mathbf{n}'' (\nabla\cdot \mathbf{n})''") = (u' * nx' + v' * ny' + w' * nz') * divn'
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sd_divn = sd' * divn'
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vn_divn_ = vn * divn
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vn_divn = vn' * divn'
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sd_divn_ = sd * divn
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divt_v (latex="\nabla_T \cdot \mathbf{v}") = (1.-nx) * ddx(u) + (1.-ny) * ddy(v) + (1.-nz) * ddz(w)
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vnsd_nx_nx_flux = vnsd_nx' * nx'
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vnsd_divn_nx_flux = vnsd_divn' * nx'
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vnsd_nx_divn_flux = vnsd_nx' * divn'
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vnsd_divn_divn_flux = vnsd_divn' * divn'
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gradtx_vnsd (latex="\nabla_{Tx} \left(v_n + S_d \right)") = (1.-nx) * ddx(vnsd)
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gradty_vnsd (latex="\nabla_{Ty} \left(v_n + S_d \right)") = (1.-ny) * ddy(vnsd)
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gradtz_vnsd (latex="\nabla_{Tz} \left(v_n + S_d \right)") = (1.-nz) * ddz(vnsd)
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lapt_vnsd (latex="\nabla^2_T \left(v_n + S_d\right)") = (1.-nx) * ddx(gradtx_vnsd) + (1.-ny) * ddy(gradty_vnsd) + (1.-nz) * ddz(gradtz_vnsd)
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vnsd_gradn_gradn = vnsd * gradn_gradn
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vnsd_nx_absk = vnsd_nx' * absk'
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vnsd_divn_absk = vnsd_divn' * absk'
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sign_lapt_vnsd = $sign(1.0, divn) * lapt_vnsd
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sign_vnsd_gradn_gradn = $sign(1.0, divn) * vnsd_gradn_gradn
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dcdn = nx * ddx(c) + ny * ddy(c) + nz * ddz(c)
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d2cdn2 = nx * ddx(dcdn) + ny * ddy(dcdn) + nz * ddz(dcdn)
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avg {
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u, v, w,
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u_lvl, v_lvl, w_lvl,
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y, c, f,
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ddx_c, ddy_c, ddz_c,
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lapc, d2dx_c, d2dy_c, d2dz_c,
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uc,
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dcdn, d2cdn2
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}
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# <>u
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avg y { u, v, w, c, f, lapc, ddx_c, ddy_c, ddz_c, d2dx_c, d2dy_c, d2dz_c }
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# <>b
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avg c { u, v, w, c, f, lapc, ddx_c, ddy_c, ddz_c, d2dx_c, d2dy_c, d2dz_c }
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# <>K
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avg d2cdn2 { nx, ny, nz }
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# <>f
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avg f {
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u, v, w,
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u_lvl, v_lvl, w_lvl,
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nx, ny, nz,
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nx2, ny2, nz2,
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nn,
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unxsd,
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vn, sd, vnsd,
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vn_lvl, sd_lvl, vnsd_lvl,
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absk, divn,
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absk_lvl, divn_lvl,
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nx_lvl, ny_lvl, nz_lvl,
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unx, vny, wnz,
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unx_fluc, vny_fluc, wnz_fluc,
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divt_v,
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vnsd_nx,
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vnsd_nx_fluc,
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vnsd_nx_lvl,
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vn_nx,
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sd_nx,
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u_nx_nx ,
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v_ny_nx ,
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w_nz_nx ,
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vnsd_divn,
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vnsd_divn_fluc,
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nx_divn,
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u_divn,
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v_n_divn,
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sd_divn,
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sd_divn_,
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vn_divn,
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vn_divn_,
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vnsd_nx_nx_flux,
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vnsd_nx_divn_flux,
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vnsd_divn_nx_flux,
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vnsd_divn_divn_flux,
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gradtx_vnsd,
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lapt_vnsd,
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vnsd_gradn_gradn,
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vnsd_divn_absk,
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sign_lapt_vnsd,
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sign_vnsd_gradn_gradn
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}
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