2025/05/24 by Luca Arpaia, Giuseppe Orlando, Arpaia, Luca +5 · 1 citation
Engineering · Earth and Planetary Sciences · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Oceanographic and Atmospheric Processes
paper · pdf · doi:10.48550/arxiv.2505.18743
We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number of mathematical properties specific to the proposed method that is well-balanced, mass-conserving and positivity-preserving under a mild CFL condition also in the presence of wet-dry fronts. The method includes a consistent conservative discretization for passive tracers. We use a high-order Discontinuous Galerkin (DG) method as implemented in the deal.II library. This environment provides efficient and native parallelization techniques and automatically handles non-conforming meshes to implement adaptive strategies which are tested in a coastal environment. Idealized test cases show the robustness in presence of irregular bathymetries also with under-resolved features at the grid scale. A benchmark with realistic bathymetry and a complex domain shows the potential of the proposed discretization for adaptive simulations of coastal flows.