On Proper Orthogonal Decomposition (POD) based Reduced-Order Modeling of Groundwater Flow through Heterogeneous Porous Media with Point Source Singularity

Abstract Groundwater, being a vital component of the natural water resource system, needs continuous monitoring and dynamic management strategies. That said, we require computationally inexpensive groundwater flow models for repetitive solutions with desirable accuracy under budgetary limitation(s). Natural aquifer systems inherit strong heterogeneity at local scales. In this work, we have proposed ordinary kriging-based sequential algorithm for generating replicates of randomly distributed heterogeneous hydraulic conductivity field (Monte Carlo method-based algorithm) conditioned by field values from sampled locations in an irregular-unstructured grid system. Finite Volume method-based groundwater models often encounter difficulties with the representation of point source/sink terms operating within the domain. In this paper, we have proposed an irregular-unstructured grid Finite Volume discretization technique for overcoming the singularity of point source/sink term to yield a consistent output with different grid dimensions. Furthermore, full-system groundwater models often come with a substantial computational burden. Hence, reduction in model order cuts down the computational expenses (in terms of CPU time and usage) to a significant level. We have also put forth a model order reduction methodology for three different illustrative pumping tests. The proposed framework for the model order reduction projects the governing groundwater flow equation on a set of identified patterns or orthonormal basis functions, applying the Galerkin Projection method to compute a vector of time-dependent coefficients. We have performed pattern identification by Singular Value Decomposition (SVD) of snapshots of full-system model simulation data at selected time instants within the pumping test time domain. The numerical results of the proposed reduced-order models show a good approximation of the full-system models at a comparatively lesser computational time. The accuracy and efficiency of the models attempt to ensure their potential applicability for identifying groundwater dynamics.