Bridging the lab- to field-scale solutions of Navier–Stokes equations to study seawater intrusion in fractures

• DOI: 10.1007/s00366-025-02115-1
• Publication Date: 2025-03-10T16:01:11Z
• Authors: Costantino Mascio...; Marco Berardi

Abstract Scale effects and mass continuity loss may affect upscaling methods that couple sequential model simulation outputs by increasing computational domains and upscaling equations coefficients or averaging representative volumes. We propose an innovative method unaffected by scale effect errors and based on ‘similarity criteria’ (SC) to upscale solutions of Navier–Stokes equations (NSEs) from the laboratory scale to a portion of the investigated aquifer. SC utilises real-world physical quantities such as forces and fluid properties (i.e. viscosity and density) to downscale a field-scale flow. Stationarity between real world (i.e. prototype) and downscaled fluid dynamics is ensured by the similarity of forces, strengths, lengths, and times of the designed building, which can be accurately reproduced in a lab-scaled model. We leverage the SC theory to apply NSEs to unsteady variable salinity water flow into the freshwater of individual fractures of coastal aquifers. Numeric simulations are conducted in an ‘in silico’ downscaled model ten times smaller than the field-scale target aquifer. The proposed SC analysis generates solutions and identifies key factors affecting the progress of seawater intrusion. Upscaled solutions of the NSEs through ‘in silico’ experiments remain largely unaffected by scale effects, producing maps of salt iso-concentration from sea intrusion and of velocity vectors. These NSE field-scale solutions cannot be obtained easily at a field scale and reveal that local small obstacles to the flow in a fracture can block sea inland advancement. Minimal discrepancies (6%) in a simulated iso-concentration contour of 10 g/l inland advancement suggest further studies to improve upscaling performances of the SC method.