A Reduced Order Model for Sea Water Intrusion Simulation Using Proper Orthogonal Decomposition

Area of Science:

• Hydrogeology
• Computational Fluid Dynamics
• Environmental Engineering

Background:

• Sustainable management of coastal aquifers relies on accurate simulation of seawater intrusion (SWI).
• Traditional variable-density flow simulators solving partial differential equations (PDEs) are computationally intensive.
• Model surrogates, particularly reduced-order models (ROMs), offer computational efficiency for evaluating management strategies.

Purpose of the Study:

• To implement and investigate a variable-density flow reduced-order model using proper orthogonal decomposition (POD) and a finite-difference (FD) approach for simulating SWI.
• To assess the accuracy and computational efficiency of the FD-POD method for both homogeneous and heterogeneous coastal aquifer systems.
• To demonstrate the compatibility of the FD-POD approach with established variable-density flow models.

Main Methods:

• Development of a fully coupled flow and solute-transport model.
• Implementation of a finite-difference (FD) approach for solving governing PDEs.
• Application of proper orthogonal decomposition (POD) to create a reduced-order model (ROM).
• Testing the FD-POD model using Henry's problem in homogeneous and heterogeneous systems.

Main Results:

• The FD-POD approach demonstrates significant computational gains compared to full-scale models.
• The method achieves high accuracy in simulating seawater intrusion (SWI) for both homogeneous and heterogeneous aquifer conditions.
• The FD-POD model effectively accommodates outputs from popular variable-density flow simulators, including MODFLOW.

Conclusions:

• The combined FD-POD approach is an effective tool for simulating SWI in coastal aquifers, balancing accuracy and computational efficiency.
• This ROM offers a valuable alternative for groundwater management scenarios requiring rapid evaluation of numerous pumping strategies.
• The FD-POD method enhances the utility of existing groundwater modeling frameworks for coastal resource management.