TY - JOUR
T1 - Improvement of generalized finite difference method for stochastic subsurface flow modeling
AU - Chen, Shang Ying
AU - Hsu, Kuo Chin
AU - Fan, Chia Ming
N1 - Funding Information:
This study was financially supported by the Ministry of Science and Technology, Taiwan (MOST) (project nos. 107-2221-M-006-033 and 108-2116-M-006-008 ). The authors wish to thank Associate Editor Nicholas Zabaras and anonymous reviewers for their suggestions and comments, which greatly improved the manuscript.
PY - 2020
Y1 - 2020
N2 - Uncertainty is embedded in groundwater flow modeling because of the heterogeneity of hydraulic conductivity and the scarcity of measurements. To quantify the uncertainty of the modeled hydraulic head, this study proposes an improved version of the meshless generalized finite difference method (GFDM) for solving the statistical moment equation (ME). The proposed GFDM adopts a new support sub-domain for calculating the derivative of the head to improve accuracy. Synthetic fields are applied to validate the proposed method. The proposed GFDM outperforms the conventional GFDM in terms of accuracy based on a comparison with the results of the finite difference method. The ME-GFDM scheme is shown to be 2.6 times faster than Monte Carlo simulation with comparable accuracy. The ME-GFDM is versatile in that it easily handles irregular domains, allows the node location and number to be changed, and allows the sequential addition of new data without remeshing, which is required for traditional mesh-based methods.
AB - Uncertainty is embedded in groundwater flow modeling because of the heterogeneity of hydraulic conductivity and the scarcity of measurements. To quantify the uncertainty of the modeled hydraulic head, this study proposes an improved version of the meshless generalized finite difference method (GFDM) for solving the statistical moment equation (ME). The proposed GFDM adopts a new support sub-domain for calculating the derivative of the head to improve accuracy. Synthetic fields are applied to validate the proposed method. The proposed GFDM outperforms the conventional GFDM in terms of accuracy based on a comparison with the results of the finite difference method. The ME-GFDM scheme is shown to be 2.6 times faster than Monte Carlo simulation with comparable accuracy. The ME-GFDM is versatile in that it easily handles irregular domains, allows the node location and number to be changed, and allows the sequential addition of new data without remeshing, which is required for traditional mesh-based methods.
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U2 - 10.1016/j.jcp.2020.110002
DO - 10.1016/j.jcp.2020.110002
M3 - Article
AN - SCOPUS:85097401676
VL - 429
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 110002
ER -