Numerical Analysis of Time Fractional-Order Unsaturated Flow and Its Application

ZHU Shuairun; LI Shaohong; ZHONG Caiyin; WU Lizhou

doi:10.21656/1000-0887.420334

Volume 43 Issue 9

Sep. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(9): 966-975

ZHU Shuairun, LI Shaohong, ZHONG Caiyin, WU Lizhou. Numerical Analysis of Time Fractional-Order Unsaturated Flow and Its Application[J]. Applied Mathematics and Mechanics, 2022, 43(9): 966-975. doi: 10.21656/1000-0887.420334

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Numerical Analysis of Time Fractional-Order Unsaturated Flow and Its Application

doi: 10.21656/1000-0887.420334

1.
State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China
2.
Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China
3.
Department of Geological Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

Received Date: 2021-11-04
Rev Recd Date: 2022-01-08

Available Online: 2022-09-08

Publish Date: 2022-09-30

Abstract

Abstract

Numerical simulation of the unsaturated flow process is of great significance to many fields such as soil slope stability analysis and migration simulation of underground pollutants. Generally, it is widely used due to the universal applicability of the Richards equation, but the seepage process described by the Richards equation does not involve the anomalous diffusion phenomenon in natural environment and experiments. To address this problem, the Caputo derivative was applied to obtain the time fractional-order Richards equation with broader seepage significance. Then the finite difference method was used to get the discretization scheme and the Picard method was chosen to solve it iteratively, and the sensitivity analysis of the fractional parameters and soil-water characteristic curves was carried out. Finally, combined with the experimental data of soil column infiltration, the numerical solutions obtained from the time fractional-order Richards equation under different soil-water characteristic curves were compared. The results show that, the time fractional-order Richards equation of the VGM model has better fitting effects for the measured data and can better describe the seepage process of groundwater in unsaturated soil.
- unsaturated flow,
- Richards equation,
- time fractional-order,
- finite difference,
- soil column experiment

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References(37)

References

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