From 75dd9b43baa4152e15c2aa2ea2c8d118d5119bd9 Mon Sep 17 00:00:00 2001
From: Martin Schneider <martin.schneider@iws.uni-stuttgart.de>
Date: Tue, 16 Jul 2024 18:15:09 +0200
Subject: [PATCH] [ex][basic][slides] Define darcys law as a velocity
---
slides/problem.md | 8 ++++----
1 file changed, 4 insertions(+), 4 deletions(-)
diff --git a/slides/problem.md b/slides/problem.md
index caba4fa3..9c921aea 100644
--- a/slides/problem.md
+++ b/slides/problem.md
@@ -14,8 +14,8 @@ Mass balance equations for two fluid phases:
$$
\begin{aligned}
\frac{\partial \left(\phi \varrho_\alpha S_\alpha \right)}{\partial t}
- -
- \nabla \cdot \boldsymbol{v}_\alpha
+ +
+ \nabla \cdot \left(\varrho_\alpha \boldsymbol{v}_\alpha \right)
-
q_\alpha = 0, \quad \alpha \in \lbrace w, n \rbrace.
\end{aligned}
@@ -24,7 +24,7 @@ $$
Momentum balance equations (multiphase-phase Darcy's law):
$$
\begin{aligned}
-\boldsymbol{v}_\alpha = \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\nabla\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right), \quad \alpha \in \lbrace w, n \rbrace.
+\boldsymbol{v}_\alpha = -\frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\nabla\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right), \quad \alpha \in \lbrace w, n \rbrace.
\end{aligned}
$$
@@ -59,7 +59,7 @@ $$
$$
* Constitutive relations: $p_n := p_w + p_c$, $p_c := p_c(S_w)$, $k_{r\alpha}$ = $k_{r\alpha}(S_w)$
-* Physical constraint (no free space): $S_w + S_n = 1$
+* Physical constraint: $S_w + S_n = 1$
* Primary variables: $p_w$, $S_n$ (wetting phase pressure, non-wetting phase saturation)
--
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