Finite element method for subsurface hydrology using a mixed explicit‐implicit scheme

The mixed explicit‐implicit Galerkin finite element method developed previously by the authors is shown to be ideally suited for a wide class of problems arising in subsurface hydrology. These problems include confined saturated flow, unconfined flow under free surface conditions subject to the Dupuit assumption, flow in aquifers which are partly confined and partly unconfined, axisymmetric flow to a well with storage, and flow in saturated‐unsaturated soils. A single computer program, entitled Flump, can now handle all of these problems. The mixed explicit‐implicit solution strategy employed in the program insures a high level of accuracy and computation efficiency in most cases. It eliminates many of the difficulties that groundwater hydrologists have been encountering in trying to simulate extensive aquifer systems by finite elements. Some of the outstanding features of this solution strategy include an automatic control of time step size, reclassification of nodes from explicit to implicit during execution, automatic adjustment of the implicit time‐weighting factor, and the treatment of boundary conditions and source terms as arbitrary functions of time of the state of the system. Five examples are presented to demonstrate the versatility and power of this new approach. A purely physical derivation of the finite element equations which does not rely on the Galerkin formalism is also included in one of the appendices. This paper is not subject to U.S. copyright. Published in 1978 by the American Geophysical Union.