Efficient Implementation of Tidal Forcing in Simulations of Groundwater Dynamics in Subterranean Estuaries

Submarine groundwater discharge from subterranean estuaries is affected by tides, which are represented in computational models as time-dependent boundary conditions on the seaward boundary. Conventionally, a small time step is used in the numerical model to phase-resolve the tidal signal so as to ensure accurate results, although at the cost of excessive computation times for long-term simulations. This study proposes a highly efficient alternative method for modeling the tidal signal, in which a phase-averaged pressure is assigned to the seawater boundary with a much larger time step. The assigned pressure condition is first determined from an analytical solution of the time-independent pressure boundary condition. Along with the analytical solution, a single calibration factor is introduced at the beach face to account for the conductance at the beach. This results in good agreement between the results for phase-averaged and phase-resolved simulations. The new method is verified by comparison of the results for a wide range of physical cases determined using TOUGHREACT, a model for simulating coupled hydrodynamic, thermodynamic, and geochemical processes. This comparison shows that the phase-averaged results give good agreement except for a small underestimation of the mixing zone over the saltwater wedge region. These results confirm that the new boundary condition is suitable for efficient, long-term simulations of coastal aquifers subjected to tidal forcing.