Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
D
dorie
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
33
Issues
33
List
Boards
Labels
Service Desk
Milestones
Merge Requests
11
Merge Requests
11
Analytics
Analytics
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Commits
Issue Boards
Open sidebar
dorie
dorie
Commits
84c235f3
Commit
84c235f3
authored
Jan 31, 2019
by
Lukas Riedel
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Update user docs for initial conditions
parent
63255b37
Changes
1
Pipelines
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
40 additions
and
33 deletions
+40
-33
doc/man-initial.rst
doc/man-initial.rst
+40
-33
No files found.
doc/man-initial.rst
View file @
84c235f3
...
...
@@ -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
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment