Gradual Variation Analysis for Groundwater Flow. (arXiv:1001.3190v1 [math.NA])

Groundwater flow in Washington DC greatly influences the surface water
quality in urban areas. The current methods of flow estimation, based on
Darcy's Law and the groundwater flow equation, can be described by the
diffusion equation (the transient flow) and the Laplace equation (the
steady-state flow). The Laplace equation is a simplification of the diffusion
equation under the condition that the aquifer has a recharging boundary. The
practical way of calculation is to use numerical methods to solve these
equations. The most popular system is called MODFLOW, which was developed by
USGS. MODFLOW is based on the finite-difference method in rectangular Cartesian
coordinates. MODFLOW can be viewed as a "quasi 3D" simulation since it only
deals with the vertical average (no z-direction derivative). Flow calculations
between the 2D horizontal layers use the concept of leakage. In this project,
we have established a mathematical model based on gradually varied functions
for groundwater data volume reconstruction. These functions do not rely on the
rectangular Cartesian coordinate system. A gradually varied function can be
defined in a general graph or network. Gradually varied functions are suitable
for arbitrarily shaped aquifers. Two types of models are designed and
implemented for real data processing: (1) the gradually varied model for
individual (time) groundwater flow data, (2) the gradually varied model for
sequential (time) groundwater flow data. In application, we also established a
MySQL database to support the related research. The advantage of the gradually
varied fitting and its related method does not need the strictly defined
boundary condition as it is required in MODFLOW.

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Original source : http://arxiv.org/abs/1001.3190...