A numerical procedure for the solution of the steady state variable density groundwater flow equation

Abstract

A numerical code is developed for the solution of the three‐dimensional steady state groundwater flow equation in which groundwater density varies with spatial position and is treated as known spatially dependent parameter. The integrated finite difference grid elements of the numerical code are rectangular when viewed along the vertical direction, but their top and bottom surfaces parallel or are coincident with the interfaces between the geologic strata within the solution region. Conditions that are sufficient for the accuracy of the code are derived. Approximate solutions for pressure head, as determined from the code, are compared for accuracy with several exact analytic test solutions.

Variable‐density flow in the midcontinent basins and arches region of the United States

“…The threedimensional, variable-density flow code VARDEN, developed by the U.S. Geological Survey [Kuiper, 1983[Kuiper, , 1985, was used because it meets the objectives of our study: analysis of steady state, variable-density hydrodynamics at a regional scale. VARDEN has been used to simulate regional variable-density flow in the Gulf Coast aquifer system [Williamson et al, 1990] and in the Palo Duro Basin of Texas [Kelley, 1989].…”

Numerical techniques for simulating groundwater flow in the presence of temperature gradients

“…Therefore, modflow cannot be used to simulate convective groundwater flow. The variable density flow modification of modflow [6] is not applicable either, since it ignores coupling between heat and mass transfer processes.…”

Regional Aquifer-System Analysis Program of the U.S. Geological Survey: Summary of projects, 1978-84

“…The model probably will consist of 11 aquifers; however, the details of how each aquifer will be delineated has not been finalized. Flow of ground water in all of the aquifers, with the exception of the Upper Cretaceous aquifer, will be simulated using a variable-density flow model developed by Kuiper (1983). Spatial variation in water density and water temperature, is .…”

“…For example, a multiaquifer-well simulation technique was developed during the Northern Midwest RASA study (Bennett and others, 1982). An improved method of simulating variable-density ground-water flow also has been 7 developed by Weiss (1982) and Kuiper (1983). The RASA Program also supports research by specialists within the Geological Survey in areas of geohydrology and geochemistry.…”