An Adaptive Local Time-Stepping Method Applied to Storm Surge Inundation Simulation

This study proposes an adaptive local time stepping (LTS) method based on a two-dimensional shallow water model for simulating multi-scale storm surge inundation in coastal regions. By dynamically monitoring the variation in the proportion of dry/wet cells during the simulation, the method adaptively adjusts the maximum local time step level, improving computational efficiency and minimizing human intervention in traditional LTS schemes. Through a series of idealized cases, this paper derives an empirical criterion for selecting the maximum LTS level and performs detailed analysis for two typical scenarios: in the absence of dry cells, the optimal LTS level is based on the maximum local time step under quiescent conditions; in complex hydrodynamic models with dry cells, the adaptive adjustment strategy based on the dry cell proportion is required to handle the increased computational complexity. The results show that when the proportion of dry cells was between 40% and 70%, the maximum LTS level increased by one level, and when it exceeded 70%, the maximum LTS level increased by two levels, with a recommended maximum limit of 7 levels. In ideal cases, the adaptive LTS method improves efficiency, with speedups of up to 5.83 times compared to traditional methods. Furthermore, the adaptive LTS method is successfully applied to storm surge and seawater inundation simulations, with validation through comparison with observational data. In particular, the simulation of the seawater backflow event in Erjiegou demonstrated the method’s ability to capture both the occurrence time and extent of seawater backflow, confirming its efficiency and reliability in complex hydrodynamic processes. The proposed method holds significant promise for applications in storm surge forecasting, disaster assessment, and emergency management.