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A non-linear mathematical model for an undisturbed soil-column experiment and source parameter identification. (English) Zbl 1351.80011

Summary: We put forward a nonlinear transport model for an undisturbed soil-column experiment with the nonlinear Freundlich’s isotherm. As compared with ordinary models based on linear adsorption, the retardation factor is a nonlinear functional of solute concentration, and the production term is a nonlinear term related with the solute concentration and an unknown source/sink function. Furthermore, an actual undisturbed soil-column experiment in Zibo, Shandong Province, China is investigated, and an inverse problem of identifying the source/sink parameter is considered with the additional data of breakthrough curves. An optimal perturbation iteration algorithm is applied to determine the unknown source/sink parameter both in the cases of accurate and inaccurate data. The inversion results show that the optimal perturbation algorithm is efficient at least to the problem of this article, and the nonlinear mathematical model here could be applied to describe undisturbed soil-column experiments with nonlinear adsorption behaviours.

MSC:

80A32 Chemically reacting flows
80A23 Inverse problems in thermodynamics and heat transfer
35R30 Inverse problems for PDEs
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
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References:

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