Open Access

ARTICLE

A Quasi-Boundary Semi-Analytical Method for Backward in Time Advection-Dispersion Equation

Chein-Shan Liu¹, Chih-Wen Chang², Jiang-Ren Chang^2,3

1 Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan
2 Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan
3 Corresponding author, Tel.: +886-2-24622192x6031. E-mail: cjr@mail.ntou.edu.tw

Computers, Materials & Continua 2009, 9(2), 111-136. https://doi.org/10.3970/cmc.2009.009.111

Abstract

In this paper, we take the advantage of an analytical method to solve the advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is employed to calculate the concentration field C(x, t) at any time t< T. Then, we consider a direct regularization by adding an extra term αC(x,0) on the final condition to carry off a second kind Fredholm integral equation. The termwise separable property of the kernel function permits us to transform itinto a two-point boundary value problem. The uniform convergence and error estimate of the regularized solution C^α(x,t) are provided and a strategy to select the regularized parameter is suggested. The solver used in this work can recover the spatial distribution of the groundwater contaminant concentration. Several numerical examples are examined to show that the new approach can retrieve all past data very well and is good enough to cope with heterogeneous parameters’ problems, even though the final data are noised seriously.

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Keywords

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