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A galerkin finite-element flow model to predict the transient response of a radially symmetric aquifer. Abstract 1 Introduction 1 Model assumptions and capabilities 1 Theory 2 Solution of radial flow equation by Galerkin finite-element method 2 Boundary conditions 5 Matrix equations 6 Computer program 7 Main 7 Subroutine CHECK 8 Subroutine MLTBM 8 Subroutine SOLVE 8 Evaluation of the model 8 Comparison with analytical solutions 8 Comparison with model solutions 9 Observations on model behavior 10 Possible program modifications 10 Design considerations for the finite-element grid 11 Sample simulation 11 Conclusions 13 References cited 13 Supplemental Data: I. Fortran IV program listing 16 II. Definition of selected program variables 24 III. Data input formats 25 IV. Array dimensioning 27 V. Input data for test problem 28 VI. Selected output for test problem 32 FIGURES 1. Diagram showing conceptual model of aquifer flow system 1 2. Diagram of modeled aquifer section showing configuration of triangular elements 3 3. Diagram showing typical linear triangular basis function 4 4-7. Graphs showing: 4. Comparison of model results with Theis' dimensionless analytical solution 9 5. Comparison of model results with Hantush 's analytical solution for head buildup in aquifer directly beneath center of a circular recharge basin and at 500 ft from basin center 10 6. Comparison of water-table drawdowns as predicted by Stallman's analog model and the Galerkin finite-element model 11 7. Comparison of drawdowns at the base of an aquifer as predicted by Stallman's analog model and the Galerkin finite-element model 12 8. Diagram showing radial cross section of aquifer for sample simulation 13

A Galerkin finite-element flow model to predict the transient response of a radially symmetric aquifer