An Invariant-region-preserving (IRP) Limiter to DG Methods for Compressible Euler Equations
For computational fluid dynamics practitioners, this provides a robust limiter that ensures physical admissibility without sacrificing accuracy, though it is an incremental improvement over existing limiters.
The paper introduces an explicit limiter for DG methods that preserves invariant regions (positivity of density/pressure and entropy maximum principle) for compressible Euler equations, maintaining high-order accuracy and damping oscillations near discontinuities.
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.