Groundwater:Formulation

Trescott and Larson (1977) described the solution to the two-dimensional free surface groundwater problem, and the efficiency of various solvers. Their methods were largely followed in the development of this portion of the code; an exhaustive coverage need not be presented here. The overall approach, differences in approach, and integration into the GSSHA model are presented.

The controlling equation, as developed by Pinder and Bredehoeft (1968), is:

(40)

where:

T is the transmissivity (m²/s),

h is the hydraulic head (m),

S is the storage term (dimensionless),

and W is the flux term for sources and sinks (m/s).

It is assumed that off diagonal terms are not important and that transmissivity can be expressed as the product of the saturated hydraulic conductivity of the media (K) and the depth of the saturated media (b). For the free surface problem the head is the surface water elevation (E_ws).

(41)

This equation can be represented using a block-centered finite difference five-point implicit scheme as:

(42)

This representation varies from the original representation of Trescott and Larson (1977) in that the transmissivities and the storage terms are both time dependent and calculated implicitly using Picard iteration.