Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations

  • Authors:

  • Cheng Wang;Xiangxiong Zhang;Chi-Wang Shu;Jianguo Ning

  • Affiliations:

  • State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, PR China;Department of Mathematics, Brown University, Providence, RI 02912, United States;Division of Applied Mathematics, Brown University, Providence, RI 02912, United States;State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, PR China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

One of the main challenges in computational simulations of gas detonation propagation is that negative density or negative pressure may emerge during the time evolution, which will cause blow-ups. Therefore, schemes with provable positivity-preserving of density and pressure are desired. First order and second order positivity-preserving schemes were well studied, e.g., [6,10]. For high order discontinuous Galerkin (DG) method, even though the characteristicwise TVB limiter in [1,2] can kill oscillations, it is not sufficient to maintain the positivity. A simple solution for arbitrarily high order positivity-preserving schemes solving Euler equations was proposed recently in [22]. In this paper, we first discuss an extension of the technique in [22-24] to design arbitrarily high order positivity-preserving DG schemes for reactive Euler equations. We then present a simpler and more robust implementation of the positivity-preserving limiter than the one in [22]. Numerical tests, including very demanding examples in gaseous detonations, indicate that the third order DG scheme with the new positivity-preserving limiter produces satisfying results even without the TVB limiter.