A multiscale algorithm for soil water flow and solute transport simulations and its application in subsurface drainage system optimization

Networks of subsurface pipes are widely used in humid regions to facilitate rapid removal of surface ponding and effectively decrease groundwater tables. Their application is also extended to arid regions as a strategic approach for mitigating soil salinization. Currently available subsurface pipe layout design methods require updating to properly incorporate salt discharge in such contexts. Numerical modeling is then a key tool for effective optimization of design parameters of such subsurface drainage systems. One of the challenges in subsurface drainage simulation is the inherent multiscale nature of the setting. A substantial scale disparity can be evidenced between millimeter-scale dimensions of subsurface drainage pipes and the meter-scale size of available field-scale soil profiles. Gradients of water potential and solute concentration near a subsurface pipe are typically high, thus challenging accuracy of numerical simulations targeting water and salt content across the soil-water system. To achieve accurate and computationally efficient simulations of water flow and solute transport in soil-water system within which subsurface drainage systems are in place, implementation of local grid refinement strategies is critical. In this context, we proposed (Qian et al., 2024) a soil water flow and solute transport model based on a vertex- centered finite volume method (VCFVM). The model has virtually no limitations on the cell shape as well as the number of neighbor cells, and strictly ensures local mass conservation. Here, we start by rigorously assessing the accuracy and efficiency of the algorithm upon considering test scenarios characterized by various soil textures and diverse boundary conditions. Our results show the that accurate solutions can be obtained upon relying on a grid whose number of nodes is only 5% of that of globally refined grid of the kind that are typically employed. The model is then further integrated with drainage equations to accurately simulate subsurface drainage process, so that the effect of placement of subsurface pipes can be effectively included. Our study suggests that the proposed model can accurately simulate soil water content, solute concentration, and subsurface drainage amount using a typical (globally refined) gridding procedure. Otherwise, it can save about 95% of CPU time by using nonmatching grids. Finally, a novel, user-friendly framework for the optimization of subsurface pipe layouts and corresponding leaching quota is proposed and demonstrated on a series of exemplary scenarios.

Reference:
Yingzhi Qian, Xiaoping Zhang, Yan Zhu, Lili Ju, Alberto Guadagnini, Jiesheng Huang, 2024, A novel vertex-centered finite volume method for solving Richards' equation and its adaptation to local mesh refinement, Journal of Computational Physics, 501, 112766,
https://doi.org/10.1016/j.jcp.2024.112766.