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# 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

APA Style
Chang, C., Liu, C. (2010). A quasi-boundary semi-analytical approach for two-dimensional backward advection-dispersion equation. Computers, Materials & Continua, 17(1), 19-40. https://doi.org/10.3970/cmc.2010.017.019
Vancouver Style
Chang C, Liu C. A quasi-boundary semi-analytical approach for two-dimensional backward advection-dispersion equation. Comput Mater Contin. 2010;17(1):19-40 https://doi.org/10.3970/cmc.2010.017.019
IEEE Style
C. Chang and C. Liu, "A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Advection-Dispersion Equation," Comput. Mater. Contin., vol. 17, no. 1, pp. 19-40. 2010. https://doi.org/10.3970/cmc.2010.017.019

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