1-D, 2-D, and 3-D analytical solutions of unsaturated flow in groundwater |
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| Authors: | Fred T Tracy |
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| Institution: | US Army Engineer Waterways Experiment Station, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA |
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| Abstract: | An excellent tool for checking numerical models of unsaturated flow in groundwater is analytical solutions. However, because of the highly nonlinear nature of the governing partial differential equation, only a limited number of analytical solutions are available. This paper first gives some simple 1-D solutions. Next, by use of a transformation, the nonlinear partial differential equation is converted to a linear one for a specific form of the moisture content vs. pressure head and relative hydraulic conductivity vs. pressure head curves. This allows both 2-D and 3-D solutions to be derived, which is done in this paper. Finally, computations from a finite element computer program are compared with results from one of the analytical solutions to illustrate the use of the derived equations. |
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