From 6bde00c1257b84adea686ee34533e2ec6b8b15f8 Mon Sep 17 00:00:00 2001 From: Omotayo Omosebi Date: Mon, 19 Aug 2019 14:06:10 -0400 Subject: [PATCH] Explains formulation of the saturation equation --- doc/news/changes/minor/20190807Omosebi | 4 ++++ examples/step-21/doc/intro.dox | 8 ++++---- 2 files changed, 8 insertions(+), 4 deletions(-) create mode 100644 doc/news/changes/minor/20190807Omosebi diff --git a/doc/news/changes/minor/20190807Omosebi b/doc/news/changes/minor/20190807Omosebi new file mode 100644 index 0000000000..bd9cca8ea1 --- /dev/null +++ b/doc/news/changes/minor/20190807Omosebi @@ -0,0 +1,4 @@ +Changed: The saturation equation in step-21 is explained further for +consistency with literatures in porous media transport. +
+(Omotayo Omosebi, 2019/08/07) diff --git a/examples/step-21/doc/intro.dox b/examples/step-21/doc/intro.dox index 543c69f6a7..4fa98411d9 100644 --- a/examples/step-21/doc/intro.dox +++ b/examples/step-21/doc/intro.dox @@ -79,13 +79,13 @@ of course is going to change as the fluids move around. The second part of the equations is the description of the dynamics of the saturation. The saturation equation for the displacing fluid (water) is: @f{eqnarray*} - S_{t} + \nabla \cdot (F(S) \mathbf{u}) = \{q}_{w}, + S_{t} + \nabla \cdot (F(S) \mathbf{u}) = q_{w}, \\ - S_{t} + F(S) \nabla \mathbf{u} + \mathbf{u} \cdot \nabla F(S) = S_{t} + F(S) * \q + \mathbf{u} \cdot \nabla F(S) = \{q}_{w}. + S_{t} + F(S) \nabla \mathbf{u} + \mathbf{u} \cdot \nabla F(S) = S_{t} + F(S) * q + \mathbf{u} \cdot \nabla F(S) = q_{w}. @f} -where $\{q}_{w}$ is the flow rate of the displacing fluid (water) and is related to the fractional flow F(S) through: +where $q_{w}$ is the flow rate of the displacing fluid (water) and is related to the fractional flow F(S) through: @f[ - \{q}_{w} = F(S) * \q, + q_{w} = F(S) * q, \\ F(S) = -- 2.39.5