Commit 84c235f3 authored by Lukas Riedel's avatar Lukas Riedel

Update user docs for initial conditions

parent 63255b37
......@@ -25,35 +25,39 @@ They are controlled by the ``initial.type`` key and available for every model.
* ``type = analytic``
This type of initial condition defines an analytic function
:math:`f(x,y,z)` by the keyword ``initial.equation``.
.. math::
f(x,y,z)
Possible variables
* ``x``
* ``y``
* ``z`` (Only in 3D)
* ``pi``
* ``dim``
Possible operations
* The mos common ones. Check out the complete list in muParser_.
.. _muParser: http://beltoforion.de/article.php?a=muparser&p=features
Richards
For instance, for Richards simulations it is useful to
set a gravity flow regime with the equation ``-y``
(or ``-z``) for 2 (or 3) dimensions.
Transport
Another example is to set a pulse in the middle of the domain for the
solute concentration in the transport model, in such case, the a possible
equation may be
``exp(-sqrt((x-0.5)^2+(y-0.5)^2)/(4.*0.002))/(4*pi*0.002)^(2/dim)``.
An analytic function :math:`f(\vec{p})` which depends on the physical
position :math:`\vec{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).
* ``h``: Height above origin. Synonymous to ``y`` in 2D and ``z`` in 3D.
* ``pi``: Mathematical constant :math:`\pi`.
* ``dim``: Number of physical dimensions.
.. tip::
Assuming the target quantity is the matric head (see
: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}`::
initial.equation = -h + <v>
* Gravity flow: Constant value.
.. tip::
The expression for a gaussian pulse of solute concentration centered at
:math:`\vec{p} = [0.5, 0.5]^T \, \mathrm{m}` is::
initial.equation = exp(-sqrt((x-0.5)^2+(y-0.5)^2)/(4.*0.002))/(4*pi*0.002)^(2/dim).
.. _initial-transformation:
Transformation Types
--------------------
......@@ -68,8 +72,8 @@ Initial condition tranformations for the Richards solver.
* ``quantity = matricHead``
The input data is directly interpreted as matric head
:math:`h_m [\mathrm{m}]`.
The input data is directly interpreted as matric head,
:math:`f = h_m [\mathrm{m}]`.
Transport
^^^^^^^^
......@@ -79,5 +83,8 @@ Initial condition tranformations for the Transport solver.
* ``quantity = soluteConcentration``
The input data is directly interpreted as solute concentration
:math:`c_w`.
The input data is directly interpreted as solute concentration,
:math:`f = c_w`.
.. _muparser: http://beltoforion.de/article.php?a=muparser&p=features
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