laws:hypofe2
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laws:hypofe2 [2023/11/24 10:12] 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 $y$ $(=f_{gy})$| | ||
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| ===== State variables ===== | ===== State variables ===== | ||
| ==== Number of state variables ==== | ==== Number of state variables ==== | ||
| - | = 9 | + | 10 + 5*(Number of Subscale Nodes)\\ |
| + | /!\ The state variables vector also contains the following information for each subscale node: X,Y,Pw,C,Pg | ||
| ==== List of state variables ==== | ==== List of state variables ==== | ||
| - | |Q(1)|water relative permeability $(=k_{rw})$ | | + | |Q(1)|Liquid water mass at the RVE| |
| - | |Q(2)|air relative permeability $(=k_{ra})$ | | + | |Q(2)|Pollutant mass at the RVE| |
| - | |Q(3)|Soil porosity (= n) | | + | |Q(3)|Gaseous air mass at the RVE| |
| - | |Q(4)|Soil saturation degree $(=S_w)$ | | + | |Q(4)|Homogenised macroscale porosity| |
| - | |Q(5)|Suction $(=p_c = p_a-p_w)$ | | + | |Q(5)|Water saturation degree| |
| - | |Q(6)|water specific mass $(=\rho_w)$ | | + | |Q(6)|Homogenised water relative permeability| |
| - | |Q(7)|air specific mass $(=\rho_a)$ | | + | |Q(7)|Homogenised gas relative permeability| |
| - | |Q(8)|"Pe number" = convective effect / conductive effect \[= \frac{\rho_f . c_f . T . \vec{q}}{\Gamma_{av} . \vec{grad} (T)}\]| | + | |Q(8)|Homogenised macroscale tortuosity| |
| - | |Q(9)|Water content (=w) | | + | |Q(9)|Vapour mass at the RVE (unused)| |
| - | |Q(10)|Vapour specific mass $(=\rho_v)$ | | + | |Q(10)|Homogenised succion| |
| - | |Q(11)|Vapour pressure $(=p_v)$ | | + | |Q(11 + (i-1)*5)|$X_i$| |
| - | |Q(12)|Relative humidity $(=H_r)$ | | + | |Q(11 + (i-1)*5 +1)|$Y_i$| |
| - | |Q(13)|Liquid water mass per unit soil volume | | + | |Q(11 + (i-1)*5 +2)|$P_{w,i}$| |
| - | |Q(14)|Dry air mass per unit soil volume | | + | |Q(11 + (i-1)*5 +3)|$C_i$| |
| - | |Q(15)|Vapour mass per unit soil volume | | + | |Q(11 + (i-1)*5 +4)|$P_{g,i}$| |
| - | |Q(16)|Intrinsic permeability | | + | |
| - | |Q(17)|Gas soil saturation degree $(=S_g)$ | | + | |
| - | |Q(18)|$\alpha (H_2, N_2, …)$ partial pressure $(=p_a^g = p^g - p_{H_2O}^g = \text{gas pressure-vapour pressure})$ | | + | |
| - | |Q(19)|Area associated to one integration point | | + | |
| - | |Q(20)|Dissolved air concentration $=\frac{\rho_{a-d}}{\rho_w + \rho_{a-d}} = \frac{H_a \rho_a}{\rho_w + H_a \rho_a}$| | + | |
| - | |Q(21)|$K_{xx}$ (or zero if IANI = 0) | | + | |
| - | |Q(22)|$K_{yy}$ (or zero if IANI = 0) | | + | |
| - | |Q(23)|$K_{xy}$ (or zero if IANI = 0) | | + | |
| - | |Q(24)|$\varepsilon_1$ | | + | |
| - | |Q(25)|$\varepsilon_2$ | | + | |
| - | |Q(26)|$\alpha$ (= angle between principal stress and horizontal) | | + | |
laws/hypofe2.1700817140.txt.gz · Last modified: 2023/11/24 10:12 by arthur
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