Revision as of 09:09, 4 December 2007

analytic and analytic element solutions (Strack,1989 classification)

horizontal confined flow

one-dimensional flow

radial flow

two-dimensional flow

shallow unconfined flow

one-dimensional flow

two-dimensional flow

combined shallow confined and unconfined flow

one-dimensional flow

radial flow

shallow unconfined flow with rainfall

shallow interface flow

aquifers with vertically varying hydraulic conductivity

shallow flow in aquifers with clay laminae

shallow interface flow in aquifers with impermeable laminae

shallow semiconfined flow

shallow flow in systems of aquifers separated by leaky layers

transient shallow flow

two-dimensional flow in the vertical plane

three-dimensional flow

analytical solutions (Bruggeman,1999 classification)

Phreatic groundwater

Governing Equation (1D or 2D):

<math>\nabla \cdot \left(kh \nabla h\right)=S_y\frac{\partial h}{\partial t}-N </math>

Where <math>S_y</math> is the specific yield [-], <math>N</math> is the vertical influx to the aquifer (recharge/leakage) [<math>LT^{-1}</math>], and <math>h</math> [<math>L</math>] is both the head and the saturated thickness (i.e., the head is measured with the respect to a flat aquifer base).

A common transformation to linearize the steady state form of the equation is to solve the problem in terms of the Girinskii Potential:

<math>\Phi=\frac{1}{2}k h^2</math>

Leaving us with a revised governing equation (the Poisson equation):

<math>\nabla ^2\Phi=-N </math>

Exact solutions

One-dimensional horizontal flow

Two-dimensional radial-symmetric horizontal flow

General two-dimensional horizontal flow

Confined groundwater

Governing Equation (1D or 2D): <math>\nabla \cdot \left(kH \nabla h\right)=S_sH\frac{\partial h}{\partial t}-N </math>

Where <math>S_s</math> is the specific storage [-], <math>N</math> is the vertical influx to the aquifer (recharge/leakage) [<math>LT^{-1}</math>], <math>H</math> is the saturated thickness of the aquifer and <math>h</math> [<math>L</math>] is the head, measured with respect to an arbitrary datum.

For piecewise constant properties, we can substitute in the confined Girinskii potential (<math>\Phi=kHh</math>) to obtain the following governing equation:

<math>\nabla ^2\Phi=\frac{1}{\alpha}\frac{\partial \Phi}{\partial t}-N </math>

Where <math>\alpha=\frac{k}{S_s}</math> is the hydraulic diffusivity [<math>LT^{-1}</math>]of the aquifer.

One-dimensional flow

Two-dimensional radial-symmetric flow

General two-dimensional flow

Three-dimensional spherical flow

Three-dimensional axial-symmetric flow

General three-dimensional flow

Multi-layer systems

Dispersion

Density flow (interface)