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Initial commit of richards equation code. Forward working. Inverse untested.
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@@ -1,5 +1,9 @@
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.. _api_Richards:
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Richards Equation
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*****************
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There are two different forms of Richards equation that differ
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on how they deal with the non-linearity in the time-stepping term.
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@@ -8,7 +12,7 @@ The most fundamental form, referred to as the
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.. math::
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\\frac{\partial \\theta(\psi)}{\partial t} - \\nabla \cdot k(\psi) \\nabla \psi - \\frac{\partial k(\psi)}{\partial z} = 0
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\frac{\partial \theta(\psi)}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
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\quad \psi \in \Omega
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where theta is water content, and psi is pressure head.
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@@ -21,7 +25,7 @@ equation can be written in the continuous form as:
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.. math::
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\\frac{\partial \\theta}{\partial \psi}\\frac{\partial \psi}{\partial t} - \\nabla \cdot k(\psi) \\nabla \psi - \\frac{\partial k(\psi)}{\partial z} = 0
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\frac{\partial \theta}{\partial \psi}\frac{\partial \psi}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
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\quad \psi \in \Omega
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However, it can be shown that this does not conserve mass in the discrete formulation.
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