A MATHEMATICAL MODEL FOR TRANSIENT FREE SURFACE FLOW IN NONHOMOGENEOUS OR ANISOTROPIC POROUS MEDIA

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Abstract
A mathematical model was developed to solve a steady free surface flow problem and a rapid drawdown problem in a two‐dimensional porous medium. The same problem was also solved by an analogue device and excellent agreement was found to exist between the two solutions. This paper contains the formulation of the numerical problem from first principles and a discussion of measures that had to be taken in order to assure numerical stability and proper convergence of the solution.Although the scope of this study was limited to a two‐dimensional flow case, the elements of simulation discussed are general in nature and applicable to three‐dimensional problems. It was demonstrated that numerical solution can be obtained for the position of the free surface at given time intervals, for the piezometric head distribution within the flow field and for flow quantities across given boundaries. In addition, the mathematical model will permit consideration of nonhomogeneous or anisotropic characteristics of the porous medium, without difficulty.It is concluded that mathematical models, incorporating some or all of the techniques discussed in this paper, in conjunction with some analogue control device, can be very efficient and reliable tools for solving complex porous flow problems, including those which, so far, have eluded comprehensive analysis, due to physical and/or cost limitation.

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