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Mathematics > Numerical Analysis

arXiv:1804.08825 (math)
[Submitted on 24 Apr 2018]

Title:An invariant-region-preserving limiter for DG schemes to isentropic Euler equations

Authors:Yi Jiang, Hailiang Liu
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Abstract:In this paper, we introduce an invariant-region-preserving (IRP) limiter for the p-system and the corresponding viscous p-system, both of which share the same invariant region. Rigorous analysis is presented to show that for smooth solutions the order of approximation accuracy is not destroyed by the IRP limiter, provided the cell average stays away from the boundary of the invariant region. Moreover, this limiter is explicit, and easy for computer implementation. A generic algorithm incorporating the IRP limiter is presented for high order finite volume type schemes as long as the evolved cell average of the underlying scheme stays strictly within the invariant region. For any high order discontinuous Galerkin (DG) scheme to the p-system, sufficient conditions are obtained for cell averages to stay in the invariant region. For the viscous p-system, we design both second and third order IRP DG schemes. Numerical experiments are provided to test the proven properties of the IRP limiter and the performance of IRP DG schemes.
Comments: 28 pages, 3 figures, 9 tables, accepted for publication in Numerical Methods for Partial Differential Equations, 2018
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M60, 35L65, 35L45
Cite as: arXiv:1804.08825 [math.NA]
  (or arXiv:1804.08825v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1804.08825
Related DOI: https://doi.org/10.1002/num.22274

Submission history

From: Yi Jiang [view email]
[v1] Tue, 24 Apr 2018 03:09:31 UTC (100 KB)
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