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# Numerical Inversion of a Time-Dependent Reaction Coefficient in a Soil-Column Infiltrating Experiment

Gongsheng Li1, De Yao2, Hengyi Jiang3, Xianzheng Jia1
Institute of Applied Mathematics, Shandong University of Technology, Zibo, 255049, China.
Institute of Mining Technolgy, Inner Mongolia University of Technology, Hohhot, 010051, China.
Institute of Environmental Science and Technolgy, Shandong University of Technology, Zibo,255049, China.

Computer Modeling in Engineering & Sciences 2011, 74(2), 83-108. https://doi.org/10.3970/cmes.2011.074.083

### Abstract

This paper deals with an inverse problem of determining a time-depen -dent reaction coefficient arising from a disturbed soil-column infiltrating experiment based on measured breakthrough data. A purpose of doing such experiment is to simulate and study transport behaviors of contaminants when they vertically penetrating through the soils. Data compatibility of the inverse problem is discussed showing a sufficient condition to the solution's monotonicity and positivity with the help of an adjoint problem. Furthermore, an optimal perturbation regularization algorithm is applied to solve the inverse problem, and two typical numerical examples are presented to support the inversion algorithm. Finally, transport model of a positive solute ion in the soil-column is investigated based on the researches to the inverse problem. An optimal reaction coefficient is determined by the inversion algorithm, and the inversion is of numerical uniqueness. The inversion results not only coincide with data compatibility of the inverse problem, but also agree with the real breakthrough data.

### Keywords

solute transport, advection-dispersion equation, inverse problem, determination of time-dependent reaction coefficient, soil-column experiment, optimal perturbation regularization algorithm, numerical inversion, numerical uniqueness.

Li, G., Yao, D., Jiang, H., Jia, X. (2011). Numerical Inversion of a Time-Dependent Reaction Coefficient in a Soil-Column Infiltrating Experiment. CMES-Computer Modeling in Engineering & Sciences, 74(2), 83–108.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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