Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes

Publikationstyp:
Zeitschriftenaufsatz
Metadaten:
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Autoren-URL
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000681504000001&DestLinkType=FullRecord&DestApp=WOS_CPL
DOI
10.1007/s42967-021-00148-z
eISSN
2661-8893
Externe Identifier
  • Clarivate Analytics Document Solution ID: 2O2PC
ISSN
2096-6385
Ausgabe der Veröffentlichung
3
Zeitschrift
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
Schlüsselwörter
  • Entropy conservation
  • Kinetic energy preservation
  • Pressure equilibrium preservation
  • Compressible Euler equations
  • Local linear stability
  • Summation-by-parts
Paginierung
880 - 903
Datum der Veröffentlichung
2022
Status
Published
Titel
Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes
Sub types
  • Article
Ausgabe der Zeitschrift
4

Datenquelle: Web of Science (Lite)

Andere Metadatenquellen:
Abstract
<jats:title>Abstract</jats:title><jats:p>Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible Euler equations. The issue is related to missing local linear stability, i.e., the stability of the discretization towards perturbations added to a stable base flow. This is strongly related to an anti-diffusion mechanism, that is inherent in entropy-conserving two-point fluxes, which are a key ingredient for the high-order discontinuous Galerkin extension. In this paper, we investigate if pressure equilibrium preservation is a remedy to these recently found local linear stability issues of entropy-conservative/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler equations. Pressure equilibrium preservation describes the property of a discretization to keep pressure and velocity constant for pure density wave propagation. We present the full theoretical derivation, analysis, and show corresponding numerical results to underline our findings. In addition, we characterize numerical fluxes for the Euler equations that are entropy-conservative, kinetic-energy-preserving, pressure-equilibrium-preserving, and have a density flux that does not depend on the pressure. The source code to reproduce all numerical experiments presented in this article is available online (<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="doi" xlink:href="10.5281/zenodo.4054366">https://doi.org/10.5281/zenodo.4054366</jats:ext-link>).</jats:p>
Autoren
DOI
10.1007/s42967-021-00148-z
eISSN
2661-8893
ISSN
2096-6385
Ausgabe der Veröffentlichung
3
Zeitschrift
Communications on Applied Mathematics and Computation
Sprache
en
Online publication date
2021
Paginierung
880 - 903
Datum der Veröffentlichung
2022
Status
Published
Herausgeber
Springer Science and Business Media LLC
Herausgeber URL
http://dx.doi.org/10.1007/s42967-021-00148-z
Datum der Datenerfassung
2022
Titel
Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes
Ausgabe der Zeitschrift
4

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