MDL updating docs and docs_sphinx

doc/ADI_scheme.org

@@ -1,6 +1,7 @@
 #+TITLE: Finite Difference Schemes for the numerical solution of heterogeneous diffusion equation in 2D
 #+LaTeX_CLASS_OPTIONS: [a4paper,10pt]
 #+LATEX_HEADER: \usepackage{fullpage}
+#+LATEX_HEADER: \usepackage{charter}
 #+LATEX_HEADER: \usepackage{amsmath, systeme, cancel, xcolor}
 #+OPTIONS: toc:nil
 

doc/ValidationHetDiff.org

@@ -1,12 +1,12 @@
-#+TITLE: 2D Validation Examples
+#+TITLE: Validation Examples for 2D Heterogeneous Diffusion
 #+AUTHOR: MDL <delucia@gfz-potsdam.de>
-#+DATE: 2023-07-31
+#+DATE: 2023-08-26
 #+STARTUP: inlineimages
 #+LATEX_CLASS_OPTIONS: [a4paper,9pt]
 #+LATEX_HEADER: \usepackage{fullpage}
 #+LATEX_HEADER: \usepackage{amsmath, systeme}
 #+LATEX_HEADER: \usepackage{graphicx}
-#+LATEX_HEADER: \usepackage{}
+#+LATEX_HEADER: \usepackage{charter}
 #+OPTIONS: toc:nil
 
 
@@ -38,7 +38,7 @@ constant in 4 quadrants:
 The relevant part of the R script used to produce these results is
 presented in listing 1; the whole script is at [[file:scripts/HetDiff.R]].
 A visualization of the output of the reference simulation is given in
-figure [[#fig:1][1]].
+figure [[fig:1][1]].
 
 Note: all results from this script are stored in the =outc= matrix by
 the =deSolve= function. I stored a different version into
@@ -47,6 +47,7 @@ for each time step including initial conditions) and 121 rows, one for
 each domain element, with no headers.
 
 #+caption: Result of ReacTran/deSolve solution of the above problem at 4
+#+name: fig:1
 [[./images/deSolve_AlphaHet1.png]]
 
 

docs_sphinx/index.rst

@@ -5,12 +5,25 @@
 
 Welcome to Tug's documentation!
 ===============================
+
 Welcome to the documentation of the TUG project, a simulation program
-for solving one- and two-dimensional diffusion problems with heterogeneous diffusion coefficients, more 
+for solving transport equations in one- and two-dimensional uniform
-generally, for solving the following differential equation
+grids using cell centered finite differences.
+
+Diffusion
+-----------
+
+TUG can solve diffusion problems with heterogeneous and anisotropic
+diffusion coefficients. The partial differential equation expressing
+diffusion reads:
 
 .. math::
-   \frac{\partial C}{\partial t} = \alpha_x \frac{\partial^2 C}{\partial x^2} + \alpha_y \frac{\partial^2 C}{\partial y^2}.
+   \frac{\partial C}{\partial t} =  \nabla \cdot \left[ \mathbf{\alpha} \nabla C \right]
+
+In 2D, the equation reads:
+   
+.. math::
+   \frac{\partial C}{\partial t} =  \frac{\partial}{\partial x}\left[ \alpha_x \frac{\partial C}{\partial x}\right] + \frac{\partial}{\partial y}\left[ \alpha_y \frac{\partial C}{\partial y}\right]
 
 .. toctree::
    :maxdepth: 2