Commit c25cd5dd authored by Lukas Riedel's avatar Lukas Riedel

Homogenize user docs on initial conditions

* Use \mathbf to indicate vectors instead of \vec.
* Use \text instead of \mathrm for improved text rendering.
* Add formula for vertical gradient.
parent 951ad67b
......@@ -31,16 +31,16 @@ They are controlled by the ``initial.type`` key and available for every model.
* ``type = analytic``
An analytic function :math:`f(\vec{p})` which depends on the physical
position :math:`\vec{p}`. The function must be defined via the key
An analytic function :math:`f(\mathbf{p})` which depends on the physical
position :math:`\mathbf{p}`. The function must be defined via the key
``initial.equation``. For parsing the input expression, we use muparser_
which supports a set of common mathematical functions. Additionally, the
following variables can be used:
Available variables:
* ``x``: X-coordinate :math:`p_1 \, [\mathrm{m}]`.
* ``y``: Y-coordinate :math:`p_2 \, [\mathrm{m}]`.
* ``z``: Z-coordinate :math:`p_3 \, [\mathrm{m}]` (only in 3D).
* ``x``: X-coordinate :math:`p_1 \, [\text{m}]`.
* ``y``: Y-coordinate :math:`p_2 \, [\text{m}]`.
* ``z``: Z-coordinate :math:`p_3 \, [\text{m}]` (only in 3D).
* ``h``: Height above origin. Synonymous to ``y`` in 2D and ``z`` in 3D.
* ``pi``: Mathematical constant :math:`\pi`.
* ``dim``: Number of physical dimensions.
......@@ -50,8 +50,9 @@ They are controlled by the ``initial.type`` key and available for every model.
:ref:`initial-transformation`), typical initial conditions for a
Richards simulation are
* Hydrostatic equilibrium: A vertical gradient of :math:`-1` and a
fixed value ``<v>`` at height :math:`h = 0 \, \mathrm{m}`::
* Hydrostatic equilibrium: A vertical gradient of
:math:`\partial_h h_m = -1` and a fixed value ``<v>`` at height
:math:`h = 0 \, \text{m}`:
initial.equation = -h + <v>
......@@ -59,7 +60,7 @@ They are controlled by the ``initial.type`` key and available for every model.
.. tip::
The expression for a gaussian pulse of solute concentration centered at
:math:`\vec{p} = [0.5, 0.5]^T \, \mathrm{m}` is::
:math:`\mathbf{p} = [0.5, 0.5]^T \, \text{m}` is::
initial.equation = exp(-sqrt((x-0.5)^2+(y-0.5)^2)/(4.*0.002))/(4*pi*0.002)^(2/dim).
......@@ -95,7 +96,7 @@ Initial condition tranformations for the Richards solver.
* ``quantity = matricHead``
The input data is directly interpreted as matric head
:math:`f = h_m \, [\mathrm{m}]`.
:math:`f = h_m \, [\text{m}]`.
.. object:: Water Content to Matric Head
......@@ -121,7 +122,7 @@ Initial condition tranformations for the Transport solver.
* ``quantity = soluteConcentration``
The input data is directly interpreted as solute concentration,
:math:`f = c_w [\mathrm{kg}/\mathrm{m}^3]`.
:math:`f = c_w [\text{kg}/\text{m}^3]`.
.. _H5: https://www.h5py.org/
.. _muparser: http://beltoforion.de/article.php?a=muparser&p=features
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