  Finite difference method and finite element method are popular methods for
solving groundwater flow equations. This paper presents a new method that uses
gradually varied functions to solve such equation. In this paper, 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 used two sets of
real data and one set of experimental data to test our methods.
