Semi-implicit schemes for modeling water flow and solute transport in unsaturated soils

IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Advances in Water Resources Pub Date : 2024-10-11 DOI:10.1016/j.advwatres.2024.104835
Hamza Kamil , Abdelaziz Beljadid , Azzeddine Soulaïmani , Yves Bourgault
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Abstract

The coupled model of water flow and solute transport in unsaturated soils is addressed in this study. Building upon previous research findings by Keita, Beljadid, and Bourgault, we investigate a class of second-order time-stepping techniques where two free parameters are introduced, to identify the most stable and accurate scheme. The spatial discretization of the Richards equation is accomplished using the mixed finite element method. The proposed approach involves formulating noniterative schemes using an extrapolation formula and Taylor approximation in time to linearize nonlinear terms. Additionally, a specialized regularization technique is applied to ensure the convergence of the proposed numerical methods. Numerical simulations are conducted to determine the optimal scheme for solving the Richards equation, which is subsequently extended to the transport equation.
Numerical simulations of water flow reveal the good accuracy of three schemes—SBDF, MSBDF, and Richards-M2 for homogeneous and heterogeneous soils. Notably, the SBDF scheme stands out for its computational efficiency and stability, especially when gravity forces dominate over capillary forces. Through numerical analysis of the coupled semi-implicit schemes, our results affirm the SBDF scheme’s superior robustness, establishing it as the optimal choice among the proposed numerical methods. Therefore, the SBDF scheme is employed to solve the coupled model of water flow and solute transport. We conducted various numerical experiments to solve the coupled model, addressing scenarios including single and multispecies nitrogen transport, pore water electrical conductivity, and nitrate transport. The SBDF scheme’s accuracy was rigorously verified through comparisons with reference solutions and experimental data. This establishes the SBDF scheme as an efficient alternative to traditional implicit methods for modeling water flow and solute transport in unsaturated soils.
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非饱和土壤中水流和溶质迁移建模的半隐式方案
本研究探讨了非饱和土壤中水流和溶质迁移的耦合模型。在 Keita、Beljadid 和 Bourgault 先前研究成果的基础上,我们研究了一类引入两个自由参数的二阶时间步进技术,以确定最稳定、最精确的方案。理查兹方程的空间离散化采用混合有限元法完成。所提出的方法包括使用外推法和泰勒近似法制定非迭代方案,在时间上对非线性项进行线性化。此外,还采用了专门的正则化技术,以确保所提数值方法的收敛性。水流的数值模拟表明,对于均质和异质土壤,三种方案--SBDF、MSBDF 和 Richards-M2 都具有良好的精度。值得注意的是,SBDF 方案在计算效率和稳定性方面表现突出,尤其是当重力大于毛细力时。通过对耦合半隐式方案的数值分析,我们的结果肯定了 SBDF 方案的优越稳健性,使其成为所提出的数值方法中的最佳选择。因此,我们采用 SBDF 方案来求解水流和溶质输运耦合模型。我们进行了各种数值试验来求解耦合模型,解决了包括单种群和多种群氮输运、孔隙水电导率和硝酸盐输运在内的各种情况。通过与参考解和实验数据的比较,我们严格验证了 SBDF 方案的准确性。这证明 SBDF 方案是模拟非饱和土壤中水流和溶质迁移的传统隐式方法的有效替代方案。
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来源期刊
Advances in Water Resources
Advances in Water Resources 环境科学-水资源
CiteScore
9.40
自引率
6.40%
发文量
171
审稿时长
36 days
期刊介绍: Advances in Water Resources provides a forum for the presentation of fundamental scientific advances in the understanding of water resources systems. The scope of Advances in Water Resources includes any combination of theoretical, computational, and experimental approaches used to advance fundamental understanding of surface or subsurface water resources systems or the interaction of these systems with the atmosphere, geosphere, biosphere, and human societies. Manuscripts involving case studies that do not attempt to reach broader conclusions, research on engineering design, applied hydraulics, or water quality and treatment, as well as applications of existing knowledge that do not advance fundamental understanding of hydrological processes, are not appropriate for Advances in Water Resources. Examples of appropriate topical areas that will be considered include the following: • Surface and subsurface hydrology • Hydrometeorology • Environmental fluid dynamics • Ecohydrology and ecohydrodynamics • Multiphase transport phenomena in porous media • Fluid flow and species transport and reaction processes
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