laws:hypofe2
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laws:hypofe2 [2023/11/24 10:20] arthur [Number of state variables] |
laws:hypofe2 [2023/11/29 13:51] (current) arthur [The model] |
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| - | ====== HYPOFE2 **(WIP)**====== | + | ====== HYPOFE2 ====== |
| ===== Description ===== | ===== Description ===== | ||
| Multiscale law for water-air seepage, pollutant diffusion and advection. Inspired from WAVAT and ADVEC. | Multiscale law for water-air seepage, pollutant diffusion and advection. Inspired from WAVAT and ADVEC. | ||
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| - Intrinsic Permeability $k_w$: \\ Depending on the water saturation degree $S_w$ : $k_{r,w} = f(S_w)$ with $k_{w,eff} = k_f k_{r,w}$ | - Intrinsic Permeability $k_w$: \\ Depending on the water saturation degree $S_w$ : $k_{r,w} = f(S_w)$ with $k_{w,eff} = k_f k_{r,w}$ | ||
| - Saturation degree $S_w$: \\ Depending on succion $s = p_a - p_w : S_w = f(s)$ | - Saturation degree $S_w$: \\ Depending on succion $s = p_a - p_w : S_w = f(s)$ | ||
| + | |||
| + | === Saturation degree equation (with FKRSAT) === | ||
| + | ISR = 53 Van Genuchten model (ISR=5) with hysteresis implemented. | ||
| + | |||
| + | The main water retention curves (d=drying, w=wetting) are, according to the Van Genuchten model: | ||
| + | \[S_{ed} = S_{res} + (S_{max}-S_{res}) \left[1 + \left(\frac{s}{a_d}\right)^{n_d}\right]^{-m_d}\] | ||
| + | \[S_{ew} = S_{res} + (S_{max}-S_{res}) \left[1 + \left(\frac{s}{a_w}\right)^{n_w}\right]^{-m_w}\] | ||
| + | |||
| + | The hysteresis is then defined by: | ||
| + | \[\frac{\partial S_{es}}{\partial s} (\text{wetting}) = \left(\frac{s_w}{s}\right)^b\left(\frac{\partial S_{ew}}{\partial s}\right) \text{ with } s_w = a_w \left(S_e^{-1/m_w}\right)^{1/n_w}\] | ||
| + | \[\frac{\partial S_{es}}{\partial s} (\text{drying}) = \left(\frac{s_d}{s}\right)^{-b}\left(\frac{\partial S_{ed}}{\partial s}\right) \text{ with } s_d = a_d \left(S_e^{-1/m_d}\right)^{1/n_d}\] | ||
| + | |||
| + | And therefore: | ||
| + | \[S_e^{t+1} = S_e^t + \left(\frac{\partial S_{es}}{\partial s}\right)\times ds\] | ||
| + | |||
| + | The ISR=53 parameters are: CSRW1=$a_d$, CSRW2=$n_d$, CSRW3=$a_w$, CSRW4=$n_w$ and CSRW5=$b$ | ||
| === Mass conservation of dry air === | === Mass conservation of dry air === | ||
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| With C_M and C_m [-] the concentration in pollutant at the macroscale and subscale, respectively. $v_i^w$ is the water velocity obtained from Darcy's law and $D$ [m$^2$/s] is the diffusion and dispersion coefficient. | With C_M and C_m [-] the concentration in pollutant at the macroscale and subscale, respectively. $v_i^w$ is the water velocity obtained from Darcy's law and $D$ [m$^2$/s] is the diffusion and dispersion coefficient. | ||
| ==== Files ==== | ==== Files ==== | ||
| - | Prepro: LHYPOFE2.F & EHYPOFE2A.F\\ | + | Prepro: LHYPOFE2.F \\ |
| - | Lagamine: HYPOFE2.F & EHYPOFE2B.F\\ | + | Lagamine: HYPOFE2.F \\ |
| ===== Availability ===== | ===== Availability ===== | ||
| |Plane stress state| NO | | |Plane stress state| NO | | ||
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| |SIG(9)|Homogenised mean flow of the pollutant along $y$ $(=(f_{py,a}+f_{py,b})/2)$| | |SIG(9)|Homogenised mean flow of the pollutant along $y$ $(=(f_{py,a}+f_{py,b})/2)$| | ||
| |SIG(10)|Homogenised pollutant flow stored (takes advection into account) $(=f_{pe})$| | |SIG(10)|Homogenised pollutant flow stored (takes advection into account) $(=f_{pe})$| | ||
| - | |SIG(11)|Homogenised diffusive flow of the pollutant along $x$ for the current step $(=f_{px,b})| | + | |SIG(11)|Homogenised diffusive flow of the pollutant along $x$ for the current step $(=f_{px,b})$| |
| - | |SIG(12)|Homogenised diffusive flow of the pollutant along $y$ for the current step $(=f_{py,b})| | + | |SIG(12)|Homogenised diffusive flow of the pollutant along $y$ for the current step $(=f_{py,b})$| |
| |SIG(13)|Homogenised gas flow along $x$ $(=f_{gx})$| | |SIG(13)|Homogenised gas flow along $x$ $(=f_{gx})$| | ||
| |SIG(14)|Homogenised gas flow along $y$ $(=f_{gy})$| | |SIG(14)|Homogenised gas flow along $y$ $(=f_{gy})$| | ||
laws/hypofe2.1700817631.txt.gz · Last modified: 2023/11/24 10:20 by arthur
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