Documentation of a numerical code for the simulation of variable density ground-water flow in three dimensions

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This report documents a numerical code for the simulation of variable density time dependant ground-water flow in three dimensions. The ground-water density* although variable in space* is assumed to be approximately constant in time and known. The Integrated Finite Difference grid elements in the code follow the geologic strata in the modeled area. If appropriate, the determination of hydraulic head in confining beds can be deleted to decrease computation time. The strongly implicit procedure (SIP} » successive over-relaxation (SOR), and eight different preconditioned conjugate gradient (PCG) methods are used to solve the approximating equations. The use of the computer program that performs the calculations in the numerical code is emphasized. Detailed instructions are given for using the computer program^ including input data formats. An example simulation and Fortran listing of the program are included. INTRODUCTION This report documents a numerical code for the simulation of variable density time dependant ground-water flow in three dimensions. The ground-water density, although variable in space, is assumed to be approximately constant in time and known. The Integrated Finite Difference grid elements in the code are six sided and rectangular when viewed from the vertical direction. The sides of these grid elements are planar, but their top and bottom surfaces follow the curvature of the geologic strata in the modeled area. The strongly implicit procedure (SIP), successive overrelaxation (SOR), and eight different preconditioned conjugate gradient methods (PCG) (Kuiper, written commun., 1984) are used to solve the approximating equations. The ground-water flow equation with constant density is used for most ground-water flow studies. In many problems the variation in ground-water density p is sufficiently small that it can be neglected. For certain situations, however, it is necessary to treat p as a function of water pressure, salt concentration, and temperature. In some cases, particularly in a confined aquifer, the pressure at a point may change considerably with time, even though the density, temperature, and salt concentration of the water change very little. This is possible, since water density is more weakly dependent upon pressure than it is upon temperature and salt concentration. Density changes that occur due to thermal and salt transport are much slower than those that occur due to pressure changes. Thus if one is interested in the simulation of pressure for a short time period, it is a permissible approximation to regard the density as being time independent and to use the ground-water flow equatiton by itself without the solute transport or heat conduction equation. In this case, the density p( x,y,z) is regarded as being time independent and is determined either by measurement, model calibration, or other procedures, much the same as the hydraulic conductivity. After a certain time period, depending upon the circumstances, pressure changes may pass to a state of quasi equi1ibrium. This may occur in a time period which is sufficiently small that density changes, due to thermal and salt transport, are insignificant. A good approximation to this quasi-equi1ibriurn solution is the solution of the steady state ground-water flow equation, again with density p(x,y,z) independent of time. Numerical solutions of this type, although valid only for the restricted conditions given above, are far less expensive in terms of computional cost than are those for more general situations which also solve the coupled solute transport and/or heat condition equations. In this report, as with Bennett (1980) and Weiss (1982), groundwater density pis assumed to be a known function of spatial po s i t i on. THEORETICAL DEVELOPMENT The basic development of the numerical code documented in this report has been presented by Kuiper (1983), and will not be presented here. Approximating equations (17) and (28) of Kuiper (1983), for steady-state flow, are: F = AXK uu Ah (M/T) (1)