mirror of
https://github.com/wassname/simpeg.git
synced 2026-07-18 12:40:30 +08:00
organizing the docs - put the content in a content folder. put the SimPEG core api docs in core_api
This commit is contained in:
@@ -0,0 +1,47 @@
|
||||
.. _api_Richards:
|
||||
|
||||
|
||||
Richards Equation
|
||||
*****************
|
||||
|
||||
There are two different forms of Richards equation that differ
|
||||
on how they deal with the non-linearity in the time-stepping term.
|
||||
|
||||
The most fundamental form, referred to as the
|
||||
'mixed'-form of Richards Equation [Celia et al., 1990]
|
||||
|
||||
.. math::
|
||||
|
||||
\frac{\partial \theta(\psi)}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
|
||||
\quad \psi \in \Omega
|
||||
|
||||
where theta is water content, and psi is pressure head.
|
||||
This formulation of Richards equation is called the
|
||||
'mixed'-form because the equation is parameterized in psi
|
||||
but the time-stepping is in terms of theta.
|
||||
|
||||
As noted in [Celia et al., 1990] the 'head'-based form of Richards
|
||||
equation can be written in the continuous form as:
|
||||
|
||||
.. math::
|
||||
|
||||
\frac{\partial \theta}{\partial \psi}\frac{\partial \psi}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
|
||||
\quad \psi \in \Omega
|
||||
|
||||
However, it can be shown that this does not conserve mass in the discrete formulation.
|
||||
|
||||
|
||||
Here we reproduce the results from Celia et al. (1990):
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.FLOW_Richards_1D_Celia1990.run()
|
||||
|
||||
Richards
|
||||
========
|
||||
|
||||
.. automodule:: SimPEG.FLOW.Richards.Empirical
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
Reference in New Issue
Block a user