From 2c02f28b0a1465fb3f3355b4fcf157f2e68fdc30 Mon Sep 17 00:00:00 2001
From: Ann Almgren <asalmgren@lbl.gov>
Date: Wed, 17 Oct 2018 18:51:34 -0700
Subject: [PATCH] Updated fluid equations
---
docs/source/FluidEquations.rst | 17 +++++++++++++----
1 file changed, 13 insertions(+), 4 deletions(-)
diff --git a/docs/source/FluidEquations.rst b/docs/source/FluidEquations.rst
index 54faa62..892774f 100644
--- a/docs/source/FluidEquations.rst
+++ b/docs/source/FluidEquations.rst
@@ -3,12 +3,21 @@ Fluid Equations
Below are the governing equations for the fluid:
-.. math:: \frac{\partial (\epsilon_g \rho_g)}{\partial t} + \nabla \cdot (\epsilon_g \rho_g U_g) = 0
+Conservation of fluid mass:
+
+.. math:: \frac{\partial (\varepsilon_g \rho_g)}{\partial t} + \nabla \cdot (\varepsilon_g \rho_g U_g) = 0
:label: eqn::mass_cons
-.. math:: \frac{ \partial (\epsilon_g \rho_g U)}{\partial t} + \nabla \cdot (\epsilon_g \rho_g U_g U_g) + \epsilon_g \nabla p_g = \nabla \cdot \tau + {\bf g}
+Conservation of fluid momentum:
+
+.. math:: \frac{ \partial (\varepsilon_g \rho_g U)}{\partial t} + \nabla \cdot (\varepsilon_g \rho_g U_g U_g) + \varepsilon_g \nabla p_g = \nabla \cdot \tau + {\bf g}
+ + \sum_{part} \beta (V_{part} - U_g)
:label: eqn::mom_cons
-.. math:: \frac{\partial \epsilon_g}{\partial t} + \nabla \cdot (\epsilon_g U_g) = 0
- :label: eqn::mass_eps
+Conservation of fluid volume:
+
+where $\sum_{part} \beta (V_{part} - U_g)$ is the drag term in which $V_{part}$ represents the particle velocity.
+
+.. math:: \frac{\partial \varepsilon_g}{\partial t} + \nabla \cdot (\varepsilon_g U_g) = 0
+ :label: eqn::mass_vareps
--
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