2025/03/01 by Yuchang Liu, Liu, Yuchang, Wei Guo +5 · 2 citations
Earth and Planetary Sciences · Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA) #Ocean Waves and Remote Sensing
paper · pdf · doi:10.48550/arxiv.2503.00553
openalex publication_date 2025/03/01 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
We propose an entropy stable and positivity preserving discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced for hydrostatic equilibrium states. To achieve these properties, we utilize the nodal DG framework and carefully design the source term discretization using entropy conservative fluxes. Furthermore, we demonstrate that the proposed methodology is compatible with a positivity preserving scaling limiter, ensuring positivity of density and pressure under an appropriate CFL condition. To the best of our knowledge, this is the first DG scheme to simultaneously achieve these three properties with theoretical justification. Numerical examples further demonstrate its robustness and efficiency.