Angular Momentum Conserving Limiters for the Euler Equations

Abstract

Limiters that are used to stabilise the discontinuous Galerkin method fail to preserve its angular momentum conservation property. We propose a simple technique that restores the conservation of angular momentum while preserving the second-order accuracy of the scheme when paired with an explicit time integrator. Numerical experiments confirm the conservation property of the technique paired with two limiters [Giuliani and Krivodonova. 2018. “Analysis of Slope Limiters on Unstructured Triangular Meshes.” Journal of Computational Physics 374: 1–26; Giuliani and Krivodonova. 2019. “A Moment Limiter for the Discontinuous Galerkin Method on Unstructured Triangular Meshes.” SIAM Journal on Scientific Computing 41 (1): A508–A537]. We show that the technique eliminates numerical artifacts that arise from limiting solutions to the Euler equations.