Initial commit of richards equation code. Forward working. Inverse untested.

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rowanc1
2014-02-25 11:35:13 -08:00
parent beb87d1f36
commit 715bed21ce
5 changed files with 752 additions and 6 deletions
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@@ -1,5 +1,9 @@
.. _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.
@@ -8,7 +12,7 @@ The most fundamental form, referred to as the
.. math::
\\frac{\partial \\theta(\psi)}{\partial t} - \\nabla \cdot k(\psi) \\nabla \psi - \\frac{\partial k(\psi)}{\partial z} = 0
\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.
@@ -21,7 +25,7 @@ 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
\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.