土壤溶质异常输运的时间分数阶对流扩散模型
A Time-Fractional Advection-Diffusion Model for Anomalous Diffusion of Solute in Soil
摘要: 土壤系统经常表现出复杂的性质并导致溶质迁移的异常扩散。基于Skaggs等人的模型，本文研究开发蒸腾和根系吸水条件下的时间分数阶对流扩散方程(FADE)模型，以模拟根区的异常扩散并进行解析求解。模拟表明，时间分数阶对流扩散模型与整数阶对流扩散模型的数值结果在表面土壤附近出现偏差，随后随着时间的推移逐渐向下移动，偏差随深度逐渐扩大，较小的α对应较高的浓度曲线，说明土壤中溶质储层较强，导致溶质运移速度较慢，即存在亚扩散。
Abstract: Soil systems often exhibit complex properties and lead to abnormal diffusion of solute transport. Based on the model of Skaggs et al., this paper develops a time fractional advection-diffusion equation (FADE) model under transpiration and root water absorption conditions to simulate abnormal diffusion in the root zone and solves it analytically. The simulation shows that the numerical results of the time fractional advection-diffusion model and the integer advection-diffusion model deviate near the surface soil, and then gradually move downward with time. The deviation gradually expands with depth, and the smaller one corresponds to a higher concentration curve, indicating that the solute reservoir in the soil is strong, resulting in a slower solute migration rate, that is, there is sub-diffusion.
文章引用：龚权标. 土壤溶质异常输运的时间分数阶对流扩散模型[J]. 应用数学进展, 2024, 13(8): 3969-3975. https://doi.org/10.12677/aam.2024.138378

参考文献

[1] Lazarovitch, N., Vanderborght, J., Jin, Y. and van Genuchten, M.T. (2018) The Root Zone: Soil Physics and beyond. Vadose Zone Journal, 17, 1-6. [Google Scholar] [CrossRef] 
[2] Schoups, G. and Hopmans, J.W. (2002) Analytical Model for Vadose Zone Solute Transport with Root Water and Solute Uptake. Vadose Zone Journal, 1, 158-171. [Google Scholar] [CrossRef] 
[3] Kuppe, C.W., Schnepf, A., von Lieres, E., Watt, M. and Postma, J.A. (2022) Rhizosphere Models: Their Concepts and Application to Plant-Soil Ecosystems. Plant and Soil, 474, 17-55. [Google Scholar] [CrossRef] 
[4] Nishida, K. and Shiozawa, S. (2010) Modeling and Experimental Determination of Salt Accumulation Induced by Root Water Uptake. Soil Science Society of America Journal, 74, 774-786. [Google Scholar] [CrossRef] 
[5] Berardi, M., D’Abbicco, M., Girardi, G. and Vurro, M. (2022) Optimizing Water Consumption in Richards’ Equation Framework with Step-Wise Root Water Uptake: A Simplified Model. Transport in Porous Media, 141, 469-498. [Google Scholar] [CrossRef] 
[6] Young, I.M. and Crawford, J.W. (2004) Interactions and Self-Organization in the Soil-Microbe Complex. Science, 304, 1634-1637. [Google Scholar] [CrossRef] [PubMed]
[7] Brusseau, M.L. (1993) The Influence of Solute Size, Pore Water Velocity, and Intraparticle Porosity on Solute Dispersion and Transport in Soil. Water Resources Research, 29, 1071-1080. [Google Scholar] [CrossRef] 
[8] Zhang, Y., Sun, H., Stowell, H.H., Zayernouri, M. and Hansen, S.E. (2017) A Review of Applications of Fractional Calculus in Earth System Dynamics. Chaos, Solitons & Fractals, 102, 29-46. [Google Scholar] [CrossRef] 
[9] Moradi, G. and Mehdinejadiani, B. (2020) An Experimental Study on Scale Dependency of Fractional Dispersion Coefficient. Arabian Journal of Geosciences, 13, Article No. 409. [Google Scholar] [CrossRef] 
[10] Zhang, Y., Benson, D.A. and Reeves, D.M. (2009) Time and Space Nonlocalities Underlying Fractional-Derivative Models: Distinction and Literature Review of Field Applications. Advances in Water Resources, 32, 561-581. [Google Scholar] [CrossRef] 
[11] Skaggs, T.H., Jarvis, N.J., Pontedeiro, E.M., van Genuchten, M.T. and Cotta, R.M. (2007) Analytical Advection-Dis-persion Model for Transport and Plant Uptake of Contaminants in the Root Zone. Vadose Zone Journal, 6, 890-898. [Google Scholar] [CrossRef] 
[12] Zhang, Y., Zhou, D., Yin, M., Sun, H., Wei, W., Li, S., et al. (2020) Nonlocal Transport Models for Capturing Solute Transport in One‐dimensional Sand Columns: Model Review, Applicability, Limitations and Improvement. Hydrological Processes, 34, 5104-5122. [Google Scholar] [CrossRef] 
[13] Wang, Q. and Zhan, H. (2015) On Different Numerical Inverse Laplace Methods for Solute Transport Problems. Advances in Water Resources, 75, 80-92. [Google Scholar] [CrossRef] 
[14] Chen, J., Liu, F. and Anh, V. (2008) Analytical Solution for the Time-Fractional Telegraph Equation by the Method of Separating Variables. Journal of Mathematical Analysis and Applications, 338, 1364-1377. [Google Scholar] [CrossRef] 
[15] Hassanzadeh, H. and Pooladi-Darvish, M. (2007) Comparison of Different Numerical Laplace Inversion Methods for Engineering Applications. Applied Mathematics and Computation, 189, 1966-1981. [Google Scholar] [CrossRef] 
[16] Kuhlman, K.L. (2012) Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches. Numerical Algorithms, 63, 339-355. [Google Scholar] [CrossRef] 
[17] Liu, F., Meerschaert, M.M., McGough, R.J., Zhuang, P. and Liu, Q. (2013) Numerical Methods for Solving the Multi-Term Time-Fractional Wave-Diffusion Equation. Fractional Calculus and Applied Analysis, 16, 9-25. [Google Scholar] [CrossRef] [PubMed]

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