New Finite Volume–Multiscale Finite-Element Model for Solving Solute Transport Problems in Porous Media
Publication: Journal of Hydrologic Engineering
Volume 26, Issue 3
Abstract
This paper proposes a finite volume–Yeh’s finite-element–multiscale finite-element model (FVYMSFEM) for solute transport simulations, which is extended from its elliptic groundwater-flow equation scheme. The primary goals of this method are to compute advection-dominated advection-dispersion equation with high accuracy and high efficiency and to obtain continuous dispersion velocity together with concentration. The finite volume integration scheme allows the FVYMSFEM to substantially reduce the numerical dispersion and ensures local mass conservation, thus to effectively deal with a high Peclet number in advection-dominated case. Meanwhile, due to the combination of the Crank-Nicolson format and finite volume scheme, the FVYMSFEM can achieve high accurate solutions with a large time step under advection-dominated condition, even with a high Courant number. Moreover, the FVYMSFEM introduces a novel dispersion velocity matrix to transform the concentration and continuous dispersion velocity into each other, thus to calculate them in once computation. The FVYMSFEM control volume boundary flux inherits the continuity of the dispersion velocity, which leads to higher solution accuracy. In addition, similar to the multiscale finite-element method (MSFEM), the FVYMSFEM can compute solutions in a coarse-scale grid without resolving all the fine-scale features, thus saving computational effort. Some results indicate that the FVYMSFEM is more accurate than the MSFEM and conventional linear basis function finite-element method (LFEM) in advection-dominated cases. Furthermore, the FVYMSFEM can achieve the same number of concentrations as the fine grid LFEM (LFEM-F) with close accuracy while saving more than 99.8% CPU time.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Y. Xie acknowledges the financial support from the National Natural Science Foundation of China (No. 41702243) and the Fundamental Research Funds for the Central Universities (No. 2018B05114). C. Lu acknowledges the financial support from the National Key Research Project of China (2018YFC0407200), the Fundamental Research Funds for the Central Universities of China (B200204002), and the National Natural Science Foundation of China (51679067 and 51879088).
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Published In
Journal of Hydrologic Engineering
Volume 26 • Issue 3 • March 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 6, 2020
Accepted: Oct 9, 2020
Published online: Jan 7, 2021
Published in print: Mar 1, 2021
Discussion open until: Jun 7, 2021
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