diff --git a/slides/coupled_ff-pm.md b/slides/coupled_ff-pm.md
index 5ee62f16749428aebc013fce8ba0311ebbf72d8d..105f07dfdaa617c77ed70cdd88bb745990e32955 100644
--- a/slides/coupled_ff-pm.md
+++ b/slides/coupled_ff-pm.md
@@ -42,7 +42,7 @@ Fig.3 - Brain tissue (Koch et al. (2020))<sup>3</sup>
* Brain tissue
* Leaf structure
-# Model Overview
+# Model Overview
## Conceptual Physical Model
<img src=img/FFPM-PhysicalModelOverview.png width="80%">
@@ -68,8 +68,8 @@ Fig.5 - Exchange processes at the free-flow porous-medium interface at different
**Freeflow:**
-* Stokes / Navier-Stokes / RANS
-* 1-phase, n-components, non-equilibrium
+* Stokes / Navier-Stokes / RANS
+* 1-phase, n-components, non-equilibrium
**Interface condtions:**
@@ -92,7 +92,7 @@ Fig.5 - Exchange processes at the free-flow porous-medium interface at different
* Total mass balance
$$
-\frac{\partial \rho_g \textbf{v}_g}{\partial t} + \nabla \cdot (\rho_g \textbf{v}_g \textbf{v}_g^T) - \nabla \cdot (\mathbf{\tau}_g + \mathbf{\tau}_{g,t}) +\nabla \cdot (p_g\textbf{I})- \rho_g \textbf{g} = 0
+\frac{\partial \rho_g \textbf{v}_g}{\partial t} + \nabla \cdot (\rho_g \textbf{v}_g \textbf{v}_g^T) - \nabla \cdot (\mathbf{\tau}_g + \mathbf{\tau}_{g,t}) +\nabla \cdot (p_g\textbf{I})- \rho_g \textbf{g} = 0
$$
* Momentum balance
@@ -112,17 +112,17 @@ $$
* Component mass balance
$$
-\sum\limits_{\alpha \in \{\text{l, g} \}} \left(\phi \frac{\partial \left(\rho_\alpha S_\alpha X_\alpha^\kappa\right)}{\partial t } + \nabla \cdot \textbf{v}_\alpha\rho_\alpha X_\alpha^\kappa + \sum_\kappa \nabla \cdot \left( \textbf{D}_{pm,\alpha}^\kappa\rho_\alpha\nabla X_\alpha^\kappa \right)\right) = 0
+\sum\limits_{\alpha \in \{\text{l, g} \}} \left(\phi \frac{\partial \left(\rho_\alpha S_\alpha X_\alpha^\kappa\right)}{\partial t } + \nabla \cdot \textbf{v}_\alpha\rho_\alpha X_\alpha^\kappa + \sum_\kappa \nabla \cdot \left( \textbf{D}_{pm,\alpha}^\kappa\rho_\alpha\nabla X_\alpha^\kappa \right)\right) = 0
$$
* Darcy velocity
$$
-\textbf{v}_\alpha = - \frac{k_{r,\alpha}}{\mu_\alpha} K \left(\nabla p_\alpha - \rho_\alpha \textbf{g}\right)
+\textbf{v}_\alpha = - \frac{k_{r,\alpha}}{\mu_\alpha} K \left(\nabla p_\alpha - \rho_\alpha \textbf{g}\right)
$$
* Energy balance
$$
-\sum\limits_{\alpha \in \{\text{l, g} \}}\left(\phi\frac{\partial \left(\rho_\alpha S_\alpha u_\alpha\right)}{\partial t} + \nabla \cdot \left(\rho_\alpha h_\alpha \textbf{v}_\alpha \right)\right) + \left(1-\phi\right) \frac{\partial \left(\rho_s c_{p,s}T\right)}{\partial t} - \nabla\cdot \left(\lambda_{pm} \nabla T \right) = 0
+\sum\limits_{\alpha \in \{\text{l, g} \}}\left(\phi\frac{\partial \left(\rho_\alpha S_\alpha u_\alpha\right)}{\partial t} + \nabla \cdot \left(\rho_\alpha h_\alpha \textbf{v}_\alpha \right)\right) + \left(1-\phi\right) \frac{\partial \left(\rho_s c_{p,s}T\right)}{\partial t} - \nabla\cdot \left(\lambda_{pm} \nabla T \right) = 0
$$
@@ -140,24 +140,24 @@ $$
* Momentum (tangential)condition
$$
-\left[\left(- \textbf{v}_g - \frac{\sqrt{(\textbf{K}\textbf{t}_i)\cdot \textbf{t}_i}}{\alpha_{BJ}} (\nabla \textbf{v}_g + \nabla \textbf{v}_g^T)\textbf{n} \right) \cdot \textbf{t}_i \right]^{\text{ff}} = 0\, , \quad i \in \{1, .. ,\, d-1\}\,
+\left[\left(- \textbf{v}_g - \frac{\sqrt{(\textbf{K}\textbf{t}_i)\cdot \textbf{t}_i}}{\alpha_{BJ}} (\nabla \textbf{v}_g + \nabla \textbf{v}_g^T)\textbf{n} \right) \cdot \textbf{t}_i \right]^{\text{ff}} = 0\, , \quad i \in \{1, .. ,\, d-1\}\,
$$
## Mathematical Model: Coupling Conditions
* Momentum (normal) condition
$$
-[((\rho_g \textbf{v}_g \textbf{v}_g^T - (\mathbf{\tau}_g + \mathbf{\tau}_{g,t}) + p_g\textbf{I}) \textbf{n} )]^{\text{ff}} = [(p_g\textbf{I})\textbf{n}]^{\text{pm}}\,
+[((\rho_g \textbf{v}_g \textbf{v}_g^T - (\mathbf{\tau}_g + \mathbf{\tau}_{g,t}) + p_g\textbf{I}) \textbf{n} )]^{\text{ff}} = [(p_g\textbf{I})\textbf{n}]^{\text{pm}}\,
$$
* Component mass condition
$$
-[(\rho_g X_g^\kappa \textbf{v}_g + \textbf{j}_{\text{diff}, t}) \cdot \textbf{n}]^{\text{ff}} = - \left[\left( \sum_{\alpha} (\rho_{\alpha} X_{\alpha}^\kappa \textbf{v}_\alpha + \textbf{j}^\kappa_{\text{diff}, \alpha})\right) \cdot \textbf{n}\right]^{\text{pm}}\,
+[(\rho_g X_g^\kappa \textbf{v}_g + \textbf{j}_{\text{diff}, t}) \cdot \textbf{n}]^{\text{ff}} = - \left[\left( \sum_{\alpha} (\rho_{\alpha} X_{\alpha}^\kappa \textbf{v}_\alpha + \textbf{j}^\kappa_{\text{diff}, \alpha})\right) \cdot \textbf{n}\right]^{\text{pm}}\,
$$
-* Energy condition
+* Energy condition
$$
-\left[\left(\rho_g h_g \textbf{v}_g + \sum_i h_g^\kappa \textbf{j}_{\text{diff},g}^\kappa + \lambda_{g}\nabla T\right)\cdot \textbf{n}\right]^{\text{ff}} = - \left[\left( \sum_\alpha (\rho_\alpha h_\alpha \textbf{v}_\alpha + \sum_i h_\alpha^\kappa \textbf{j}_{\text{diff},\alpha}^\kappa) - \lambda_{\text{pm}}\nabla T\right)\cdot \textbf{n}\right]^{\text{pm}}\,
+\left[\left(\rho_g h_g \textbf{v}_g + \sum_i h_g^\kappa \textbf{j}_{\text{diff},g}^\kappa + \lambda_{g}\nabla T\right)\cdot \textbf{n}\right]^{\text{ff}} = - \left[\left( \sum_\alpha (\rho_\alpha h_\alpha \textbf{v}_\alpha + \sum_i h_\alpha^\kappa \textbf{j}_{\text{diff},\alpha}^\kappa) - \lambda_{\text{pm}}\nabla T\right)\cdot \textbf{n}\right]^{\text{pm}}\,
$$
## Numerical Model: Coupled Model
@@ -203,15 +203,15 @@ Fig.8 - Different evaporation stages (Or et al.(2013))<sup>6</sup>
<font size = "5">
-| Parameter | Value |
+| Parameter | Value |
|:----------------------------|--------------:|
| $\textbf{v}_g^{ff}$ [m/s] | (3.5,0)$^T$ |
-| $p_g^{ff}$ [Pa] | 1e5 |
-| $X_g^{w,ff}$ [-] | 0.008 |
-| $T^{ff}$ [K] | 298.15 |
-| $p_g^{pm}$ [Pa] | 1e5 |
-| $S_l^{pm}$ [-] | 0.98 |
-| $T^{pm}$ [K] | 298.15 |
+| $p_g^{ff}$ [Pa] | 1e5 |
+| $X_g^{w,ff}$ [-] | 0.008 |
+| $T^{ff}$ [K] | 298.15 |
+| $p_g^{pm}$ [Pa] | 1e5 |
+| $S_l^{pm}$ [-] | 0.98 |
+| $T^{pm}$ [K] | 298.15 |
</font>
@@ -264,7 +264,7 @@ _Tasks_
<font size = "5">
-1. Heck, K., Coltman, E., Schneider, J., & Helmig, R. (2020). Influence of radiation on evaporation rates: A numerical analysis. Water Resources Research, 56, e2020WR027332. https://doi.org/10.1029/2020WR027332
+1. Heck, K., Coltman, E., Schneider, J., & Helmig, R. (2020). Influence of radiation on evaporation rates: A numerical analysis. Water Resources Research, 56, e2020WR027332. https://doi.org/10.1029/2020WR027332
2. Schneider, M., Gläser, D., Weishaupt, K., Coltman, E., Flemisch, B., Helmig, R. (2023). Coupling staggered-grid and vertex-centered finite-volume methods for coupled porous-medium free-flow problems. Journal of Computational Physics. 112042. https://doi.org/10.1016/j.jcp.2023.112042.
@@ -272,8 +272,8 @@ _Tasks_
4. Fetzer, Thomas: Coupled Free and Porous-Medium Flow Processes Affected by Turbulence and Roughness – Models, Concepts and Analysis, Universität Stuttgart. - Stuttgart: Institut für Wasser- und Umweltsystemmodellierung, 2018
-5. Or, D., Lehmann, P., Shahraeeni, E. and Shokri, N. (2013), Advances in Soil Evaporation Physics—A Review. Vadose Zone Journal, 12: 1-16 vzj2012.0163. https://doi.org/10.2136/vzj2012.0163
+5. Shahraeeni, Ebrahim & Or, Dani. (2012). Coupling of evaporative fluxes from drying porous surfaces with air boundary layer: Characteristics of evaporation from discrete pores. Water Resources Research. 48. 9525-. 10.1029/2012WR011857.
-6. Or, D. (2023, 31. March). https://emeritus.step.ethz.ch/the-step-group.html
+6. Or, D., Lehmann, P., Shahraeeni, E. and Shokri, N. (2013), Advances in Soil Evaporation Physics—A Review. Vadose Zone Journal, 12: 1-16 vzj2012.0163. https://doi.org/10.2136/vzj2012.0163
-</font>
\ No newline at end of file
+</font>
diff --git a/slides/img/FFPM-SoilWaterEvapField.png b/slides/img/FFPM-SoilWaterEvapField.png
index 3a33b912e05613f9e6c54fe0436103799b473127..724408ee95d2890edd38a9055db6cd9ff05e8ca1 100644
Binary files a/slides/img/FFPM-SoilWaterEvapField.png and b/slides/img/FFPM-SoilWaterEvapField.png differ