Positivity-preserving method for high-order conservative schemes solving compressible Euler equations

Xiangyu Y. Hu, Nikolaus A. Adams, Chi Wang Shu

Research output: Contribution to journalArticlepeer-review

164 Scopus citations

Abstract

In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed for solving compressible Euler equations. The method detects critical numerical fluxes which may lead to negative density and pressure, and for such critical fluxes imposes a simple flux limiter by combining the high-order numerical flux with the first-order Lax-Friedrichs flux to satisfy a sufficient condition for preserving positivity. Though an extra time-step size condition is required to maintain the formal order of accuracy, it is less restrictive than those in previous works. A number of numerical examples suggest that this method, when applied on an essentially non-oscillatory scheme, can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.

Original languageEnglish
Pages (from-to)169-180
Number of pages12
JournalJournal of Computational Physics
Volume242
DOIs
StatePublished - 1 Jun 2013

Keywords

  • Compressible flow
  • High-order conservative scheme
  • Numerical method
  • Positivity-preserving

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