From b39d1eaa7b5381fe3c5cf73cd4b72517e702dc03 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=B6rg=20Buchwald?= <joerg.buchwald@ufz.de>
Date: Wed, 9 Dec 2020 19:48:47 +0100
Subject: [PATCH] correcting latex formulas
---
.../consolidation_pointheatsource.md | 10 +++++-----
1 file changed, 5 insertions(+), 5 deletions(-)
diff --git a/web/content/docs/benchmarks/thermo-hydro-mechanics/consolidation_pointheatsource.md b/web/content/docs/benchmarks/thermo-hydro-mechanics/consolidation_pointheatsource.md
index cf1fd7bb4be..7211af27e7c 100644
--- a/web/content/docs/benchmarks/thermo-hydro-mechanics/consolidation_pointheatsource.md
+++ b/web/content/docs/benchmarks/thermo-hydro-mechanics/consolidation_pointheatsource.md
@@ -61,10 +61,10 @@ The analytical solution of the coupled THM consolidation problem can be expresse
and
\begin{equation}
- g^{A}_{,\,i}= \dfrac{2x_{i}At}{r^{4}}\left(f^{A}-1+\dfrac{r}{\sqrt{\pi At}}\exp\left(-\dfrac{r^{2}}{4At}\right)\right),\quad i=1,2,3
+ g^{A}\_{,i} = \dfrac{2x_{i}At}{r^{4}}\left(f^{A}-1+\dfrac{r}{\sqrt{\pi At}}\exp\left(-\dfrac{r^{2}}{4At}\right)\right),\quad i=1,2,3
\end{equation}
\begin{equation}
- g^{\ast}_{,\,i} = Yg^{\kappa}_{,\,i}-Zg^{c}_{,\,i}
+ g^{\ast}\_{,i} = Yg^{\kappa}\_{,i}-Zg^{c}_{,i}
\end{equation}
For the temperature, porepressure and displacements, the correct solution can be found in the original work:
@@ -72,7 +72,7 @@ For the temperature, porepressure and displacements, the correct solution can be
\Delta T = \dfrac{Q}{4\pi Kr}f^{\kappa}
\end{equation}
\begin{equation}
- p = \dfrac{X\,Q}{\left(1-\dfrac{c}{\kappa}\right)\,4\pi Kr}\left(f^{\kappa}-f^{c}\right)
+ p = \dfrac{X\,Q}{\left(1-\dfrac{c}{\kappa}\right)4\pi Kr}\left(f^{\kappa}-f^{c}\right)
\end{equation}
\begin{equation}
u_{i} = \dfrac{Q a_\text{u}x_{i}}{4\pi Kr}\;g^{\ast}
@@ -81,10 +81,10 @@ For the temperature, porepressure and displacements, the correct solution can be
For the stress components the corrected expressions can be found in the work of Chaudhry et al. (2019):
\begin{equation}
- \sigma^{\prime}_{ij\,|\,j=i} = \dfrac{Q a_\text{u}}{4\pi Kr}\left( 2G\left[g^{\ast}\left(1-\dfrac{x^{2}_{i}}{r^{2}}\right)+x_{i}g^{\ast}_{,\,i}\right]+\lambda \left[x_{i}g^{\ast}_{,\,i}+2g^{\ast}\right]\right)-b^{\prime}\Delta T
+ \sigma^{\prime}\_{ij\,|\,j=i} = \dfrac{Q a_\text{u}}{4\pi Kr}\left( 2G\left[g^{\ast}\left(1-\dfrac{x^{2}_{i}}{r^{2}}\right)+x_{i}g^{\ast}_{,i}\right]+\lambda \left[x_{i}g^{\ast}_{,i}+2g^{\ast}\right]\right)-b^{\prime}\Delta T
\end{equation}
\begin{equation}
- \sigma^{\prime}_{ij\,|\,j \neq i} = \dfrac{Q a_\text{u}}{4\pi Kr}\left( G\left[x_{i}g^{\ast}_{,\,j}+x_{j}g^{\ast}_{,\,i}-2g^{\ast}\dfrac{x_{i}x_{j}}{r^{2}}\right]\right)
+ \sigma^{\prime}\_{ij\,|\,j \neq i} = \dfrac{Q a_\text{u}}{4\pi Kr}\left( G\left[x_{i}g^{\ast}_{,j}+x_{j}g^{\ast}_{,i}-2g^{\ast}\dfrac{x_{i}x_{j}}{r^{2}}\right]\right)
\end{equation}
## Results and evaluation
--
GitLab