Adaptive Grid Techniques for the Efficient Simulation of Shallow Coastal Systems

Introduction. Shallow coastal systems are highly dynamic and require accurate numerical models for predicting tides, storm surges, and coastal hazards. Traditional uniform-grid approaches often incur high computational costs, limiting their applicability for operational forecasting. Adaptive grid techniques provide a promising alternative by concentrating resolution in dynamically important regions while reducing the total computational burden.

Materials and Methods. We developed an adaptive-grid framework based on the depth-averaged shallow-water equations. The model employs a second-order finite-volume scheme with TVD limiting on a quadtree mesh. Mesh adaptation is driven by gradient indicators of free-surface elevation and velocity, ensuring high resolution in areas with steep gradients, tidal fronts, and complex bathymetry. Three numerical experiments were performed: a harmonic tide, a wind-driven storm surge, and combined tidal-wind forcing.

Results. The proposed method demonstrated robust wetting-drying capabilities, a mass conservation error below 0.06%, and skill metrics of RMSE ≤ 0.07 m and NSE ≥ 0.90. Compared to a uniform grid of the same finest resolution, Adaptive Mesh Refinement (AMR) reduced the mean cell count by ~32% and wall time by ~1.5×, with less than 3.5% change in the L₂ error norm.

Discussion. The results confirm that adaptive meshing preserves physical accuracy while substantially reducing computational cost. This makes the method a suitable tool for high-resolution coastal hazard assessment and operational forecasting.

Conclusion. Further work will focus on extending the approach to three-dimensional flows and incorporating data assimilation for real-time applications.

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