Table of Content

Open Access iconOpen Access

ARTICLE

A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Advection-Dispersion Equation

Chih-Wen Chang1, Chein-Shan Liu2

Grid Applied Technology Division, National Center for High-Performance Computing, Taichung40763, Taiwan. Tel.: +886-4-24620202#860. E-mail: d93510002@ntou.edu.tw
Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan. Tel.: +886-2-33664233. E-mail: liucs@ntu.edu.tw

Computers, Materials & Continua 2010, 17(1), 19-40. https://doi.org/10.3970/cmc.2010.017.019

Abstract

In this study, we employ a semi-analytical approach to solve a two-dimensional advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is used to calculate the concentration field C(x, y, t) at any time t < T. Then, we ponder a direct regularization by adding an extra termaC(x, y, 0) on the final time data C(x, y, T), to reach a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us obtaining a closed-form solution of the Fourier coefficients. A strategy to choose the regularization parameter is offered. The solver utilized in this work can retrieve the spatial distribution of the groundwater contaminant concentration. Several numerical examples are scrutinized to display that the new method can recover all the past data very well, and is good enough to deal with heterogeneous parameters, even though the final time data are noised seriously.

Keywords


Cite This Article

C. . Chang and C. . Liu, "A quasi-boundary semi-analytical approach for two-dimensional backward advection-dispersion equation," Computers, Materials & Continua, vol. 17, no.1, pp. 19–40, 2010.



cc 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.
  • 1668

    View

  • 1222

    Download

  • 0

    Like

Share Link