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.

中文翻译：

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用于模拟非饱和土壤中水流和溶质传递的半隐式方案


本研究讨论了非饱和土壤中水流和溶质运移的耦合模型。在 Keita、Beljadid 和 Bourgault 之前的研究结果的基础上，我们研究了一类二阶时间步进技术，其中引入了两个自由参数，以确定最稳定和准确的方案。Richards 方程的空间离散化是使用混合有限元方法完成的。所提出的方法涉及使用外推公式和时间泰勒近似来制定非迭代方案，以线性化非线性项。此外，应用了一种专门的正则化技术来确保所提出的数值方法的收敛性。进行数值模拟以确定求解 Richards 方程的最佳方案，该方程随后扩展到传输方程。