Improved local time-stepping schemes for storm surge modeling on unstructured grids

Abstract

This paper presents improved explicit local time-stepping (LTS) schemes of both first and second order accuracy for storm surge modeling. The two-dimensional shallow water equations are numerically solved on unstructured triangular meshes using finite volume method with Roe’s approximate Riemann solver. The LTS algorithms are designed based on explicit Euler and strong stability preserving Runge–Kutta time integration methods. A single-layer interface prediction–correction scheme is adopted to combine coarse and fine time discretization, further enhancing the stability of the LTS schemes, particularly at higher LTS levels and during long time simulations. An ideal numerical test validates the efficiency of the improved LTS models, revealing their capability to improve computational speed while preserving conservation properties and reducing accuracy loss as LTS levels increase. We further apply the LTS models to cross-scale simulations of storm surges in the Northwest Pacific. Results show that compared to the global time-stepping (GTS) models, the LTS models significantly boost computational speed by up to 37%, all while delivering equally reliable computational outcomes. With expanding high-resolution coastal data and the need for high-resolution modeling, the improved LTS models show great potential for cross-scale storm surge modeling.