95 lines
2 KiB
Text
95 lines
2 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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fsd (latex="\Sigma_f'")= sqrt (sqr(ddx(c)) + sqr(ddy(c)) + sqr(ddz(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) / fsd
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nx(latex="n_x") = - ddx(c) / fsd
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ny(latex="n_y") = - ddy(c) / fsd
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nz(latex="n_z") = - ddz(c) / fsd
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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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vn(latex="v_n") = unx + vny + wnz
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divn(latex="\nabla \cdot \vec{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 \vec{n} : \nabla \vec{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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absk = abs(divn)
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vnsd = vn+sd
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divn_nx = divn*nx
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gradn_vnsd (latex="\nabla_{\mathrm{n}}(v_n+S_d)") = ddx(vnsd) * nx + ddy(vnsd) * ny + ddz(vnsd) * nz
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gradt_vnsd1 (latex="\nabla_{\top,x}(v_n+S_d)")= ddx(vnsd) - nx * gradn_vnsd
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divn2_dndn = divn2 - gradn_gradn
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sign_divn(latex="\mathrm{sign}(\nabla \cdot \vec{n})") = $dsign(1.0, divn)
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sign_divn2_dndn = sign_divn * divn2_dndn
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vnsd_divn = vnsd * divn
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vnsd_divn_cor = vnsd' * divn'
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vnsd_divn_nx_cor = vnsd' * divn_nx'
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vnsd_divn2_dndn_cor = vnsd' * divn2_dndn'
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vnsd_sign_divn2_dndn_cor = vnsd' * sign_divn2_dndn'
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vnsd_divn_nx = vnsd * divn_nx
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vnsd_divn2_dndn = vnsd * divn2_dndn
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vnsd_sign_divn2_dndn = vnsd * sign_divn2_dndn
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vnsd_divn_nxfluc = vnsd * divn * nx'
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vnsd_divn_divnfluc = vnsd * divn * divn'
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vnsd_divn_abskfluc = vnsd * divn * absk'
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vnsd_dndn = vnsd * gradn_gradn
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sign_vnsd_dndn = sign_divn * vnsd * gradn_gradn
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avg { c, u, v, w, fsd, lapc, ddx_c, ddy_c, ddz_c, d2dx_c, d2dy_c, d2dz_c }
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avg fsd { u, v, w, nx, ny, nz, absk, divn,
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unx, vny, wnz,
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vn, sd,
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gradt_vnsd1,
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vnsd,
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vnsd_divn,
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vnsd_divn_cor,
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divn_nx,
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vnsd_divn_nx,
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vnsd_divn_nx_cor,
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divn2_dndn,
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vnsd_divn2_dndn,
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vnsd_divn2_dndn_cor,
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sign_divn2_dndn,
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vnsd_sign_divn2_dndn,
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vnsd_sign_divn2_dndn_cor,
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vnsd_divn_nxfluc,
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vnsd_divn_divnfluc,
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vnsd_divn_abskfluc,
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vnsd_dndn,
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sign_vnsd_dndn
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}
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