Roko Andricevic | PubMed Health

PubMed2003

An improved collocation method for solving the Henry problem.

The original Henry problem is characterized with severe (albeit unphysical) sea boundary condition difficult to handle with numerical methods. In this paper, we present an improved numerical solution of the Henry problem. Presented numerical model solves the steady-state dimensionless equations by the collocation method named Fup Fragment Collocation Method (FFCM) and uses R(bf) basis functions of Fup(2) (x, y) type. This method enables application of the classical formulation and high approximation accuracy as proven in comparison with published solutions. Particular difficulty in solving the original Henry problem is in the accurate representation of the seepage face due to the fixed sea concentration at the sea boundary. The results of the original Henry problem formulation and problem with modified boundary conditions indicate the accuracy and robustness of the FFCM in describing the discharge area of the considered problem.

Humans↗

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Probabilistic capture zone delineation based on an analytic solution.

A major tool used in the design of wellhead protection areas is the delineation of a capture zone for a pumping well by use of a simple, steady-state analytic solution. This simple approach has been useful for many small municipalities because of the high costs associated with obtaining the hydrogeologic information needed for detailed numerical modeling. This analytic solution, however, is deterministic, and uncertainty in the mean value estimates of the hydraulic parameters used in this model can be a major source of error in predicting capture zones. To address this problem, a statistical theory was developed for including the uncertainty in the transmissivity and the magnitude and direction of the hydraulic head gradient in the analytic solution for both the ultimate and time-dependent capture zone for an arbitrary reliability level. To demonstrate the method and investigate the effect of varying magnitudes of uncertainty on time-dependent capture zones, the method is applied to three synthetic data sets based on data from the Borden Aquifer in Ontario, Canada. In general, the results show that uncertainty in the length of the time-dependent capture zone at a given reliability level is dependent on the uncertainty in the magnitude of the mean regional flow, which is equal to the transmissivity multiplied by the hydraulic head gradient; uncertainty in the maximum width of the capture zone is dependent primarily on the uncertainty in the mean direction of the regional flow.

Equipment Design↗