Journal of Applied Mathematics
Volume 2012 (2012), Article ID 732791, 16 pages
http://dx.doi.org/10.1155/2012/732791
Research Article

Data Reconstruction for a Disturbed Soil-Column Experiment Using an Optimal Perturbation Regularization Algorithm

Gongsheng Li,1 De Yao,2 and Yongzai Wang3

1Institute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, China
2Institute of Mining Technology, Inner Mongolia University of Technology, Hohhot, Inner Mongolia 010051, China
3Analysis and Testing Center, Shandong University of Technology, Zibo, Shandong 255049, China

Received 9 August 2011; Revised 18 November 2011; Accepted 19 November 2011

Academic Editor: Morteza Rafei

Copyright © 2012 Gongsheng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with data reconstruction problem for a real disturbed soil-column experiment using an optimal perturbation regularization algorithm. A purpose of doing the experiment is to simulate and study transport behaviors of Ca2+, Na+, Mg2+, K+, S O 2 − 4 , N O − 3 , H C O − 3 , and Cl− when they vertically penetrating through sandy soils. By data analysis to breakthrough data of the eight kinds of solute ions, two kinds of models describing their transport behaviors in the column are given. One is the advection-dispersion equation with time-dependent reaction terms suitable for three ions of H C O − 3 , N O − 3 , and K+, the other is the ordinary advection-dispersion equation suitable for the rest ions. Furthermore, all the unknowns in each model are determined by utilizing the optimal perturbation regularization algorithm, respectively, and then the breakthrough data for each considered ion are reconstructed successfully. The inversion results show that the advection-dispersion model with suitable time-dependent reaction terms can be utilized to describe the experimental process and reconstruct the experimental data.