An Invariant-region-preserving (IRP) Limiter to DG Methods for Compressible Euler Equations

TL;DR

This paper presents an explicit limiter for discontinuous Galerkin methods that preserves physical invariants like positivity and entropy, ensuring high accuracy and reducing oscillations near discontinuities in compressible Euler equations.

Contribution

The paper introduces a novel invariant-region-preserving limiter for DG methods that maintains high order accuracy and physical constraints.

Findings

Limiter preserves positivity of density and pressure.

Limiter reduces oscillations near discontinuities.

High order accuracy is maintained for smooth solutions.

Abstract

We introduce an explicit invariant-region-preserving limiter applied to DG methods for compressible Euler equations. The invariant region considered consists of positivity of density and pressure and a maximum principle of a specific entropy. The modified polynomial by the limiter preserves the cell average, lies entirely within the invariant region and does not destroy the high order of accuracy for smooth solutions. Numerical tests are presented to illustrate the properties of the limiter. In particular, the tests on Riemann problems show that the limiter helps to damp the oscillations near discontinuities.