2021/04/12 by Pei Fu, Fu, Pei, Gunilla Kreiss +1 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2104.05446
openalex publication_date 2021/04/12 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28
In this paper, we develop a family of high order cut discontinuous Galerkin (DG) methods for hyperbolic conservation laws in one space dimension. The ghost penalty stabilization is used to stabilize the scheme for small cut elements. The analysis shows that our proposed methods have similar stability and accuracy properties as the standard DG methods on a regular mesh. We also prove that the cut DG method with piecewise constants in space is total variation diminishing (TVD). We use the strong stability preserving Runge-Kutta method for time discretization and the time step is independent of the size of cut element. Numerical examples demonstrate that the cut DG methods are high order accurate for smooth problems and perform well for discontinuous problems.