From db9ac5b561eb9a129131612a0f9ad5dfb823ff33 Mon Sep 17 00:00:00 2001
From: Ann Almgren <asalmgren@lbl.gov>
Date: Thu, 18 Oct 2018 15:35:02 -0700
Subject: [PATCH] Put variable definitions in a table
---
docs/source/FluidEquations.rst | 38 ++++++++++++++++------------------
1 file changed, 18 insertions(+), 20 deletions(-)
diff --git a/docs/source/FluidEquations.rst b/docs/source/FluidEquations.rst
index eda92b7..d60e9d9 100644
--- a/docs/source/FluidEquations.rst
+++ b/docs/source/FluidEquations.rst
@@ -1,25 +1,22 @@
-Fluid Equations
+Fluid Variables
===============
-We define the following fluid variables:
-
-where :math:`\rho_g =` fluid density (assumed to be constant in the absence of reactions)
-
-where :math:`\varepsilon_g =` volume fraction of fluid (accounts only for displacement of fluid by particle, does not account for the EB walls)
-
-where :math:`U_g =` fluid velocity
-
-where :math:`p_g =` fluid pressure
-
-where :math:`tau =` viscous stress tensor
+ +-----------------------+--------------------------------------------------+
+ | Variable | Definition |
+ +=======================+==================================================+
+ | :math:`\rho_g` | Fluid density |
+ +------------+-------------------------------------+-----------------------+
+ | :math:`\varepsilon_g` | Volume fraction of fluid (= 1 if no particles) |
+ +------------+-------------------------------------+-----------------------+
+ | :math:`U_g` | Fluid velocity |
+ +------------+-------------------------------------+-----------------------+
+ | :math:`\tau` | Viscous stress tensor |
+ +------------+-------------------------------------+-----------------------+
+ | :math:`g` | Gravitational acceleration |
+ +------------+-------------------------------------+-----------------------+
-where :math:`g =` gravitational acceleration
-
-where :math:`\beta_p =` drag coefficient associated with a particle
-
-where :math:`V_p =` velocity associated with a particle
-
-Below are the governing equations for the fluid:
+Fluid Equations
+===============
Conservation of fluid mass:
@@ -30,7 +27,8 @@ 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
+ \sum_{part} \beta_p (V_p - U_g) + \rho_g g
-where :math:`\sum_p \beta_p (V_p - U_g)` is the drag term in which :math:`V_p` represents the particle velocity.
+where :math:`\sum_p \beta_p (V_p - U_g)` is the drag term in which :math:`V_p` represents the particle velocity and
+ :math:`\beta_p` is the drag coefficient associated with that particle
Conservation of fluid volume:
--
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