A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 3: Design philosophy and programming details

Abstract

A MODular Finite-Element, digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water-flow. The modular structure of MODFE places the computationally independent tasks that are performed routinely by digital-computer programs simulating ground-water flow into separate subroutines, which are executed from the main program by control statements. Each subroutine consists of complete sets of computations, or modules, which are identified by comment statements, and can be modified by the user without affecting unrelated computations elsewhere in the program. Simulation capabilities can be added or modified by either adding or modifying subroutines that perform specific computational tasks, and the modular-program structure allows the user to create versions of MODFE that contain only the simulation capabilities that pertain to the ground-water problem of interest. MODFE is written in a Fortran programming language that makes it virtually device independent and compatible with desk-top personal computers and large mainframes. MODFE uses computer storage and execution time efficiently by taking advantage of symmetry and sparseness within the coefficient matrices of the finite-element equations. Parts of the matrix coefficients are computed and stored as single-subscripted variables, which are assembled into a complete coefficient just prior to solution. Computer storage is reused during simulation to decrease storage requirements. Descriptions of subroutines that execute the computational steps of the modular-program structure are given in tables that cross reference the subroutines with particular versions of MODFE. Programming details of linear and nonlinear hydrologic terms are provided. Structure diagrams for the main programs show the order in which subroutines are executed for each version and illustrate some of the linear and nonlinear versions of MODFE that are possible. Computational aspects of changing stresses and boundary conditions with time and of mass-balance and error terms are given for each hydrologic feature. Program variables are listed and defined according to their occurrence in the main programs and in subroutines. Listings of the main programs and subroutines are given.