manus_continuum_granular1

commit f647c74f68d9feff3da7a34d86586529bf7b7a89
parent d3e3eeab13f3d16f87b2c5c7bc4e806f2848d810
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date:   Tue, 25 Jun 2019 09:11:38 +0200

Rearrange solution to pore-pressure diffusion equation

Diffstat:
M
continuum-granular-manuscript1.tex
 | 
6
+++---

1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -133,11 +133,11 @@ The pore-pressure solution (Eq.~\ref{eq:p_f}) is constrained by a zero pressure 
 Here, $A$ is the forcing amplitude [Pa], $f$ is the forcing frequency [1/s], and $p_{\text{f},0}$ is the mean pore pressure over time [Pa].
 As for the granular flow solution, we also use operator splitting and finite differences to solve the equation for pore-pressure diffusion (Eq.~\ref{eq:p_f}):
 \begin{equation}
-	\Delta p_{\text{f},i} = \frac{\Delta t}{\phi_i \mu_\text{f} \beta_\text{f}}
-		\frac{1}{\Delta z}
+	\Delta p_{\text{f},i} = \frac{1}{\phi_i \mu_\text{f} \beta_\text{f}}
+		\frac{\Delta t}{\Delta z}
 		\left(
 			\frac{2 k_{i+1} k_i}{k_{i+1} + k_i} \frac{p_{i+1} - p_i}{\Delta z} -
-			\frac{2 k_{i-1} k_i}{k_{i-1} + k_i} \frac{p_i - p_{i-1}}{\Delta z}
+			\frac{2 k_i k_{i-1}}{k_i + k_{i-1}} \frac{p_i - p_{i-1}}{\Delta z}
 		\right).
 	\label{eq:p_f_solution}
 \end{equation}