Geranmehr Mohammadali, Bau Domenico, Mayer Alex S, Yu Weijiang
Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, UK.
University of Texas at El Paso, El Paso, Texas.
Ground Water. 2025 Mar-Apr;63(2):205-219. doi: 10.1111/gwat.13462. Epub 2024 Dec 27.
Sea water intrusion (SWI) simulators are essential tools to assist the sustainable management of coastal aquifers. These simulators require the solution of coupled variable-density partial differential equations (PDEs), which reproduce the processes of groundwater flow and dissolved salt transport. The solution of these PDEs is typically addressed numerically with the use of density-dependent flow simulators, which are computationally intensive in most practical applications. To this end, model surrogates are generally developed as substitutes for full-scale aquifer models to trade off accuracy in exchange for computational efficiency. Surrogates represent an attractive option to support groundwater management situations in which fast simulators are required to evaluate large sets of alternative pumping strategies. Reduced-order models, a sub-category of surrogate models, are based on the original model equations and may provide quite accurate results at a small fraction of computational cost. In this study, a variable-density flow reduced-order model based on proper orthogonal decomposition (POD) and utilizing a fully coupled flow and solute-transport model is implemented with a finite-difference (FD) approach for simulating SWI in coastal aquifers. The accuracy and computational efficiency of the FD-POD approach for both homogeneous and-more realistic-heterogeneous systems are investigated using test cases based on the classic Henry's problem (Henry 1964). The findings demonstrate that the combined FD-POD approach is effective in terms of both accuracy and computational gain and can accommodate the output of the most popular variable-density flow models, such as those from USGS's MODFLOW family.
海水入侵（SWI）模拟器是协助沿海含水层可持续管理的重要工具。这些模拟器需要求解耦合变密度偏微分方程（PDEs），以再现地下水流和溶解盐分运移的过程。这些PDEs的求解通常通过使用密度依赖流模拟器进行数值求解，在大多数实际应用中，这在计算上是密集的。为此，通常开发模型替代物来替代全尺度含水层模型，以牺牲精度来换取计算效率。替代物是支持地下水管理情况的一个有吸引力的选择，在这种情况下，需要快速模拟器来评估大量替代抽水策略。降阶模型是替代模型的一个子类别，它基于原始模型方程，并且可以以一小部分计算成本提供相当准确的结果。在本研究中，基于适当正交分解（POD）并利用完全耦合的水流和溶质运移模型的变密度流降阶模型，采用有限差分（FD）方法实现，用于模拟沿海含水层中的海水入侵。使用基于经典亨利问题（亨利，1964年）的测试案例，研究了FD-POD方法在均匀和更实际的非均匀系统中的精度和计算效率。研究结果表明，FD-POD组合方法在精度和计算增益方面都是有效的，并且可以适应最流行的变密度流模型的输出，例如美国地质调查局MODFLOW系列的模型。
