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

  • Authors:

  • Xiangyu Y. Hu;Nikolaus A. Adams;Chi-Wang Shu

  • Affiliations:

  • Lehrstuhl für Aerodynamik und Strömungsmechanik, Technische Universität München, 85748 Garching, Germany;Lehrstuhl für Aerodynamik und Strömungsmechanik, Technische Universität München, 85748 Garching, Germany;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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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.