Direct solution algorithm for the two-dimensional ground-water flow model
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Open-File Report↗
Geology topics
S. P. Larson
Publications and source records attributed to S. P. Larson.
Solution of three-dimensional groundwater flow equations using the strongly implicit procedure
A three-dimensional numerical model has been coded to use the strongly implicit procedure for solving the finite-difference approximations to the ground-water flow equation. The model allows for: (1) the representation of each aquifer and each confining bed by several layers; and (2) the use of an anisotropic hydraulic conductivity at each finite-difference block. The model is compared with a previously developed quasi-three-dimensional model by simulating the steady-state flow in an aquifer system in the Piceance Creek Basin, Colorado. The aquifer system consists of two aquifers separated by a leaky confining bed. The upper aquifer receives recharge from precipitation and is hydraulically connected to streams. For this problem, in order to make a valid comparison of results, a single layer was used to represent each aquifer. Furthermore, the need for a layer to represent the confining bed was eliminated by incorporating the effects of vertical leakage into the vertical component of the anisotropic hydraulic conductivity of the adjacent aquifers. Thus, the problem was represented by only two layers in each model with a total of about 2,100 equations. This restricted the effects of flow in the confining layer to the vertical component, but simulations with a third layer in the three-dimensional model permitting horizontal flow in the confining bed show that the two-layer approach is reasonable. Convergence to a solution of this problem takes about one minute of computer time on the IBM/155. This is about 30 times faster than the time required using the quasi-three-dimensional model.
Colorado↗
Solution of water-table and anisotropic flow problems by using the strongly implicit procedure
The use of the strongly implicit procedure (SIP) with an additional iteration parameter, β , to scale the residual vector is advantageous to the solution of some ground-waterflow problems. For steady-state water-table problems plagued by excessive elimination of grid blocks during the iteration process, selection of β <1 can be effective in limiting the deletion of blocks to a reasonable number. Also, a linear problem characterized by large anisotropy and layers of contrasting hydraulic conductivity was solved more efficiently with β =1.5. Effective values of β are generally in the range 0< β <2 and are easily determined by trial. Use of a β parameter in the SIP algorithm provides an effective solution technique for a class of ground-water-flow problems that previously was burdened by significant computational difficulty.
Journal of Research of the U.S. Geological Survey↗
Documentation of finite-difference model for simulation of three-dimensional ground-water flow
User experience has indicated that the documentation of the model of three-dimensional ground-water flow (Trescott and Larson, 1975) should be expanded. This supplement is intended to fulfill that need. The original report emphasized the theory of the strongly implicit procedure, instructions for using the groundwater-flow model, and practical considerations for application. (See also W76-02962 and W76-13085) (Woodard-USGS)
Open-File Report↗
Configuration of water table and distribution of downward leakage to the Prairie du Chien-Jordan Aquifer in the Minneapolis-Saint Paul metropolitan area, Minnesota
The configuration of the water table as plotted at a contour interval of 20 feet (6 metres) on quadrangle maps (scale 1:2,500) of the Minneapolis-Saint Paul metropolitan area. Control points used for mapping were water levels in wells, lakes and sloughs, and places where topographic contours cross perennial streams. A computer program, using a variation of Darcy's law, was developed to determine distribution of 1) downward leakage to the Prairie du Chien-Jordan aquifer under steady-state conditions, using estimated vertical-hydraulic conductivity values for overlying materials; 2) calculated vertical hydraulic conductivity values, assuming uniform leakage to the aquifer; and 3) additional leakage to the aquifer resulting from increased pumpage during the summer. For data determination and data input to the computer program, the area was gridded into units of 1-minute longitude by 1-minute latitude, about 600 acres (243 hectares) per unit. Previous work estimated the increased summer pumpage (1971) of ground water to be 127 million gallons (481x106 litres) per day. Calculations, made Within the limits of governing assumptions, indicate that 10 to 20 percent of increased summer pumpage is derived from increased leakage. Most of the remainder is probably from captured natural discharge and induced recharge from major streams within the influence of summer cones of depression. Based on available data and estimates of vertical hydraulic conductivity for geologic units, major leakage to the Prairie du Chien-Jordan aquifer is indicated to occur in formation subcrop areas, especially where these areas are. overlain by the most permeable glacial drift.
Minnesota↗