Singularities in Darcy Flow Through Porous Media

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Abstract
Several types of singularities which threaten the integrity of numerical solutions occur in potential flow problems. The singularity at the tip of a cutoff wall is strong and cannot be mistreated without unsatisfactory results. Special elements can be used to represent the analytical behavior of the potential and its derivatives. For the flow around a corner of less severity than the sheet pile the use of special elements becomes less important. The intersection between zones of an inhomogeneous aquifer represents a singularity which is similar to the cutoff wall. The interzonal singularity is weak for nonextreme differences in permeabilities and in such a case it can be ignored without a significant effect on the total solution if the numerical discretization is sufficiently fine. The presence of wells in a potential flow field produces a logarithmic singularity which can be modeled by using superposition of the analytic solution for a source in the neighborhood of the well.

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