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An Optimal control least-squares method for the solution of advection dispersion problems

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Abstract

This paper discusses the numerical solution of advection dispersion equations using an Optimal control,H 1, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeauxet al., for the solution of nonlinear fluid flow problems.

At each time step, the discretized differential equation is transformed into an optimal control problem. This problem is then stated as an equivalent minimization one, whose objective function allows the capture of the advective behavior of the equation for high values of the Pe number.

A general presentation is made of the optimization algorithm. Validation runs, for a one-dimensional example, show fairly accurate results for a wide range of Péclet and Courant numbers. Comparisons with several numerical schemes are also presented.

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Authors and Affiliations

  1. Environmental & Water Resources Engineering Ltd., PO Box 6770, 31067, Haifa, Israel

    Jacob Bensabat

  2. Israel Hydrological Service, PO Box 6381, 91063, Jerusalem, Israel

    David G. Zeitoun

Authors
  1. Jacob Bensabat
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  2. David G. Zeitoun
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Bensabat, J., Zeitoun, D.G. An Optimal control least-squares method for the solution of advection dispersion problems. Transp Porous Med 15, 129–150 (1994). https://doi.org/10.1007/BF00625513

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  • DOI: https://doi.org/10.1007/BF00625513

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