A Numerical Investigation of Transient Groundwater Flows with a Phreatic Surface Along Complex Hillslopes

AbstractMost of the existing models for analyzing unconfined flows in hillslope aquifers are based on the Boussinesq (1877) equation. In the development of these models, the assumption of negligible bed-normal velocity was employed, thus restricting their application to shallow groundwater-flow situations. On the basis of a non-hydrostatic pressure approach, a ground-water-flow model that considers the effects of the vertical curvature of the flow streamlines and the three-dimensional geometry of the underlying bedrock was proposed. A dissipative two-four finite-difference scheme was utilized to discretize and solve the model equation. The applicability of the model was assessed by conducting numerical experiments on transient unconfined flows in convergent- and divergent-type hillslope aquifers with non-uniform bedrock slopes. The numerical results for the phreatic-surface profiles and outflow discharges were compared to the experimental data, and a good agreement was obtained. The results of the comparison attested that the dynamics of the hillslope drainage processes were accurately portrayed by the proposed model. This study highlights the necessity of considering the effects of the plan shape and the profile curvature of complex hillslopes in order to improve the overall performance of the computational model.

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Documentation of computer programs to compute and display pathlines using results from the U.S. Geological Survey modular three-dimensional finite-difference ground-water flow model

Open-File Report ◽

10.3133/ofr89381 ◽

1989 ◽

Cited By ~ 100

Author(s):

David W. Pollock

Keyword(s):

Finite Difference ◽

Ground Water ◽

Water Flow ◽

Flow Model ◽

Three Dimensional ◽

Computer Programs ◽

Geological Survey ◽

Ground Water Flow ◽

The U.S

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Modeling Hydroplaning and Effects of Pavement Microtexture

Transportation Research Record Journal of the Transportation Research Board ◽

10.1177/0361198105190500118 ◽

2005 ◽

Vol 1905 (1) ◽

pp. 166-176 ◽

Cited By ~ 6

Author(s):

G. P. Ong ◽

T. F. Fwa ◽

J. Guo

Keyword(s):

Three Dimensional ◽

Flow Simulation ◽

Experimental Results ◽

Tire Pressure ◽

Finite Volume Model ◽

Proposed Model ◽

Loss Of Contact ◽

The One ◽

Theoretical Considerations ◽

Good Agreement

Hydroplaning on wet pavement occurs when a vehicle reaches a critical speed and causes a loss of contact between its tires and the pavement surface. This paper presents the development of a three-dimensional finite volume model that simulates the hydroplaning phenomenon. The theoretical considerations of the flow simulation model are described. The simulation results are in good agreement with the experimental results in the literature and with those obtained by the well-known hydroplaning equation of the National Aeronautics and Space Administration (NASA). The tire pressure–hydroplaning speed relationship predicted by the model is found to match well the one obtained with the NASA hydroplaning equation. Analyses of the results of the present study indicate that pavement microtexture in the 0.2- to 0.5-mm range can delay hydroplaning (i.e., raise the speed at which hydroplaning occurs). The paper also shows that the NASA hydroplaning equation provides a conservative estimate of the hydroplaning speed. The analyses in the present study indicate that when the microtexture of the pavement is considered, the hydroplaning speed predicted by the proposed model deviates from the speed predicted by the smooth surface relationship represented by the NASA hydroplaning equation. The discrepancies in hydroplaning speed are about 1% for a 0.1-mm microtexture depth and 22% for a 0.5-mm microtexture depth. The validity of the proposed model was verified by a check of the computed friction coefficient against the experimental results reported in the literature for pavement surfaces with known microtexture depths.

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