2024/10/22 by Yuchang Liu, Liu, Yuchang, Wei Guo +5 · 1 citation
Earth and Planetary Sciences · Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2410.16729
openalex publication_date 2024/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly controls entropy production and suppresses spurious oscillations. To address the stiffness introduced by the artificial terms, which can restrict severely time step sizes, we employ the integration factor strong stability-preserving Runge-Kutta method for time discretization. Furthermore, our method remains compatible with positivity-preserving limiters under suitable CFL conditions in extreme cases. Various numerical examples demonstrate the efficiency of the proposed scheme, showing that it maintains high-order accuracy in smooth regions and avoids spurious oscillations near discontinuities.