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Storage equation


\begin{displaymath}
\rho \; co \; \dot{p} =
k_p ( \frac{\partial^2 p}{\partial...
...}{\partial {x_3}^2} ) -
\frac{\partial v_i}{\partial x_i} + f
\end{displaymath}

Primary unknown is the groundflow_pressure $p$. Further notation: $\rho$ group_groundflow_density; $co$ group_groundflow_compressibility; $k_p$ group_groundflow_permeability; $x_i$ space coordinate; $v_i$ material velocity (if present); $f$ force_element_volume (pressure source). The equation is given for space coordinates following material velocities $v_i$ (if present).

The groundflow velocities (see groundflow_velocity) follow from:

\begin{displaymath}
{v_i}^{{\rm g}} = - k_p \frac{\partial p}{\partial x_i}
\end{displaymath}

In case of gravity, the initial nodal pressures should be initialized in the pressure part of the node_dof records, and the gravity force should be included in the pressure part of the force_element_volume record.

The above naming for $\rho$, $co$ and $k_p$ is somewhat misleading with respect to conventional naming in groundwater flow analysis. To connect better to conventional naming, we remark the following:


\begin{displaymath}
\rho co = n \beta
\end{displaymath}

where $\beta$ is the compressibility of water and $n$ is the porosity.


\begin{displaymath}
k_p = \frac{k}{\gamma_u}
\end{displaymath}

where $k$ is the permeability and $\gamma_u$ is the unit weight of water.


next up previous contents
Next: Wave equation Up: Ground water flow Previous: Ground water flow   Contents
root
1999-04-23