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An Invariant-Region-Preserving (IRP) Limiter to DG Methods for Compressible Euler Equations

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Theory, Numerics and Applications of Hyperbolic Problems II (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 237))

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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, as long as the cell average stays away from the boundary of the invariant region. 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.

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Acknowledgements

This work was supported in part by the National Science Foundation under Grant DMS1312636 and by NSF Grant RNMS (KI-Net) 1107291.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, Ames, IA, 50010, USA

    Yi Jiang & Hailiang Liu

Authors
  1. Yi Jiang
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  2. Hailiang Liu
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Correspondence to Hailiang Liu .

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Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Jiang, Y., Liu, H. (2018). An Invariant-Region-Preserving (IRP) Limiter to DG Methods for Compressible Euler Equations. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_5

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