WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

  • Authors:

  • Tao Xiong;Chi-Wang Shu;Mengping Zhang

  • Affiliations:

  • School of Mathematical Sciences, University of Science and Technology of China, Hefei, P.R. China 230026;Division of Applied Mathematics, Brown University, Providence, USA 02912;School of Mathematical Sciences, University of Science and Technology of China, Hefei, P.R. China 230026

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2012

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Abstract

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Parés, SIAM J. Numer. Anal. 44:300---321, 2006; Castro et al., Math. Comput. 75:1103---1134, 2006; J. Sci. Comput. 39:67---114, 2009). Recently, it has been observed in (Abgrall and Karni, J. Comput. Phys. 229:2759---2763, 2010) that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in (Castro et al., Math. Comput. 75:1103---1134, 2006) is proposed to improve its computational performance and to overcome some of the shortcomings. This modification is based on the high order finite volume WENO scheme with subcell resolution and it uses an exact Riemann solver to catch the right paths at the discontinuities. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach.