Galerkin simulation of hydrodynamic dispersion.

April 1974.Includes bibliographic references (pages 100-113).Also has numbering: CED73-74AP17.The problem of predicting salt-content of waters pumped by fully or partially penetrating wells in an aquifer, contaminated by salt-water intrusion on sea-coasts, indiscriminate pumping of deep saline aquifers or waste-water recharge over prolonged periods of time, has demanded the attention of hydraulic engineers and geohydrologists for the last two decades or so. This investigation is an attempt to develop a new approach for modeling such situations. A numerical simulator has been developed to represent the problem of salt-water movement induced by pumping from a saturated elastic aquifer. This simulator is based upon the Galerkin-finite-element formulations of the flow and convective-dispersion equations in cylindrical polar coordinates. Appropriate flow and convective-dispersion equations have been derived from first principles in tensorial form, taking the tensorial nature of dispersion and molecular diffusion into account. Finite-element-formulations have been developed for both the equations following the Galerkin-weighted-residual process both for the space and time domains. The flow equation formulation results in a system of symmetric matrices and that for the convective-dispersion equation in a system of non-symmetric matric es. Both these systems have been solved by Gauss-elimination. The flow and convective-dispersion equations are solved in sequence following the leap-frog-technique. The numerical simulator consists of three computer programs; MESH, FLOW and DISPER. Program MESH is an automatic generation scheme for a suitable mesh layout with triangular elements, given the geometry of the flow region. This program incorporates an optimization scheme for band-width reduction. The other two programs, FLOW and DISPER, operate in tandem. Program FLOW solves the flow equation and computes new pressures at the end of the time interval. These pressures and velocities computed from them, are used as input for program DISPER, which solves the convective-dispersion equation and calculates new concentrations. For operational simplicity program FLOW and DISPER are combined into a single program FFLOW. The validity of the simulator has been tested with known exact and approximate analytical solutions for simplified cases. Program FLOW gives comparable results with the Theis equation and Program DISPER yields values reasonably matching the solutions for radial dispersion obtained by earlier investigators. Practical application of the simulator is demonstrated by applying it to hypothetical field problems. The simulator could be used to analyze groundwater quality resulting from pumping or recharging of water from an aquifer having increased salt concentration with depth