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.

Keywords:

• Limiters
• angular momentum
• conservation
• Euler equations
• discontinuous Galerkin method

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada grant 341373-07.