From 4194fa8aed10e9bcd36cbd6717d5eccb07cf693e Mon Sep 17 00:00:00 2001
From: Dominik Kern <dominik.kern.ifgt@gmail.com>
Date: Wed, 24 Nov 2021 13:32:29 +0100
Subject: [PATCH] adapt benchmark documentation
---
.../docs/benchmarks/hydro-mechanics/InjectionProduction.md | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/web/content/docs/benchmarks/hydro-mechanics/InjectionProduction.md b/web/content/docs/benchmarks/hydro-mechanics/InjectionProduction.md
index 8085527c6d0..9bb8f8fa297 100644
--- a/web/content/docs/benchmarks/hydro-mechanics/InjectionProduction.md
+++ b/web/content/docs/benchmarks/hydro-mechanics/InjectionProduction.md
@@ -208,15 +208,15 @@ $$
where $K_\mathrm{b}$ denotes the drained bulk modulus.
Thus the weak form of the mass balance (H) depends only on pressure $p^{n,i}$ as unknown
$$
-\int_V \left( \beta\frac{p^{n,i}-p^{n,i-1}}{\Delta t}v
+\int_V \left( \beta_\mathrm{FS}\frac{p^{n,i}-p^{n,i-1}}{\Delta t}v
+S\frac{p^{n,i}-p^{n-1}}{\Delta t}v
+\frac{k}{\mu}\nabla p^{n,i} \cdot \nabla v \right) \mathrm{d}V
=\int_V \left( s v-\frac{k}{\mu}\varrho_\mathrm{f} \nabla \cdot \mathbf{g} v
-\alpha\frac{ \varepsilon_V(\mathbf{u}^{n,i-1})- \varepsilon_V(\mathbf{u}^{n-1})}{\Delta t} v \right) \mathrm{d}V,
$$
-where $\beta=\beta^\mathrm{ph}=\frac{\alpha^2}{K_\mathrm{b}}$ would correspond to the physically motivated volumetric stress.
+where $\beta_\mathrm{FS}=\beta_\mathrm{FS}^\mathrm{ph}=\frac{\alpha^2}{K_\mathrm{b}}$ would correspond to the physically motivated volumetric stress.
However, choosing another artificial volumetric stress, i.e. using a different bulk modulus than $K_\mathrm{b}$, may accelerate the convergence of the coupling iterations.
-The analysis by Mikelic and Wheeler [[2]](#2) revealed that $\beta^\mathrm{MW}=\frac{\alpha^2}{2K_\mathrm{b}}$ is generally close to the a-priori unknown optimal value $\beta^\mathrm{opt}$.
+The analysis by Mikelic and Wheeler [[2]](#2) revealed that $\beta_\mathrm{FS}^\mathrm{MW}=\frac{\alpha^2}{2K_\mathrm{b}}$ is generally close to the a-priori unknown optimal value $\beta_\mathrm{FS}^\mathrm{opt}$, for more information see [user guide - conventions]({{< ref "conventions.md#staggered-scheme" >}}).
The obtained pressure $p^{n,i}$ is then inserted into the momentum equation (M) with $\mathbf{u}^{n,i}$ as unknown
$$
--
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