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A Fictitious Time Integration Method for Backward Advection-Dispersion Equation

Chih-Wen Chang1, Chein-Shan Liu2
Grid Application Division, National Center for High Performance Computing, Taichung 40763, Taiwan
Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan. Corresponding author, E-mail address: liucs@ntu.edu.tw

Computer Modeling in Engineering & Sciences 2009, 51(3), 261-276. https://doi.org/10.3970/cmes.2009.051.261

Abstract

The backward advection-dispersion equation (ADE) for identifying the groundwater pollution source identification problems (GPSIPs) is numerically solved by employing a fictitious time integration method (FTIM). The backward ADE is renowned as ill-posed because the solution does not continuously count on the data. We transform the original parabolic equation into another parabolic type evolution equation by introducing a fictitious time coordinate, and adding a viscous damping coefficient to enhance the stability of numerical integration of the discretized equations by employing a group preserving scheme. When several numerical examples are amenable, we find that the FTIM is applicable to retrieve all past data very well and is good enough to deal with heterogeneous parameters. Even under seriously noisy final data, the FTIM is also robust against disturbance.

Keywords

Groundwater contaminant distribution, Advection-dispersion equation, Inverse problem, Fictitious time integration method (FTIM), Group preserving scheme (GPS)

Cite This Article

Chang, C., Liu, C. (2009). A Fictitious Time Integration Method for Backward Advection-Dispersion Equation. CMES-Computer Modeling in Engineering & Sciences, 51(3), 261–276.



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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