Hermite Radial Basis Collocation Method for Unsaturated Soil Water Movement Equation

Wang, Jiao; Su, Lijun; Qin, Xinqiang

doi:10.1155/2018/8298915

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…In response to the above phenomenon, the fractional Richards' equation is proposed to describe the process of water movement in unsaturated soil [1,2]. After years of research and practice, numerical simulation has become an effective technical means to simulate soil water flow and infiltration [3][4][5]. Pachepsky et al [1] used the finite difference method to solve the time fractional Richard's equation.…”

Section: Introductionmentioning

confidence: 99%

A Finite Point Method for Solving the Time Fractional Richards’ Equation

Qin

Yang

2019

Mathematical Problems in Engineering

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In this paper, we propose a numerical method for solving the time fractional Richards’ equation. We first approximate the time fractional derivative of the mentioned equations by a scheme of order O(τ2−α), 0 < a<1; then, we use the finite point method to approximate the spatial derivatives. Before the discrete spatial derivatives, we introduced the basic principles of the finite point method. We solve the one- and two-dimensional versions of these equations using the proposed method. Moreover, the stability properties of the discretized scheme related to time are theoretically analyzed. Numerical results showed the efficiency of the method presented in this paper.

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Section: Introductionmentioning

confidence: 99%

A Finite Point Method for Solving the Time Fractional Richards’ Equation

Qin

Yang

2019

Mathematical Problems in Engineering

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Numerical simulation and safety distance analysis of slope instability of ionic rare earth tailings in different rainy seasons

Geng,

Wang,

Lan

et al. 2023

Geomatics, Natural Hazards and Risk

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A Deep Learning-Based Approach for a Numerical Investigation of Soil–Water Vertical Infiltration with Physics-Informed Neural Networks

Yang

Mei

2022

Mathematics

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The infiltration of water into the soil can lead to slope instability, which is one of the important causes of many geological hazards (such as landslides and debris flows). Therefore, the numerical investigation of the soil–water infiltration process provides the prerequisite for the determination of slope stability, which is of great significance for geological hazard prevention. In this study, we propose a deep learning-based approach for a numerical investigation of soil–water vertical infiltration with physics-informed neural networks and perform a comprehensive evaluation and analysis of the soil–water infiltration process in different soil types. In the proposed approach, the partial differential equation for soil–water infiltration is combined with the neural network based on physics-informed neural networks (PINNs) to obtain numerical analysis of the soil–water infiltration process. The results indicate that (1) compared with the traditional numerical method, the PINN-based method for the numerical investigation of soil–water vertical infiltration proposed in this study has a smaller error and can obtain more accurate numerical results. (2) During vertical infiltration of water in the different soil types, the light loam is the fastest, the heavy-loam the second and the medium loam the slowest. medium-loam soils are less susceptible to water infiltration of the three soil types and are more suitable for the filling of artificial slopes and dams. The proposed approach could be employed for the simulation of soil–water infiltration processes, not only for the discrimination of slope stability under rainfall conditions, but also for the selection of artificial slopes and dams to fill soil to prevent slope instability.

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Hermite Radial Basis Collocation Method for Unsaturated Soil Water Movement Equation

Cited by 3 publications

References 22 publications

A Finite Point Method for Solving the Time Fractional Richards’ Equation

A Finite Point Method for Solving the Time Fractional Richards’ Equation

Numerical simulation and safety distance analysis of slope instability of ionic rare earth tailings in different rainy seasons

A Deep Learning-Based Approach for a Numerical Investigation of Soil–Water Vertical Infiltration with Physics-Informed Neural Networks

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