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

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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.

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Acknowledgements

We would like to thank Dr. Wei Liu for helpful discussions.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

    Tao Xiong & Mengping Zhang

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

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  1. Tao Xiong
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  2. Chi-Wang Shu
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Correspondence to Chi-Wang Shu.

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Dedicated to Professor Saul Abarbanel on the occasion of his 80th birthday.

C.-W. Shu was supported by ARO grant W911NF-11-1-0091 and NSF grant DMS-1112700.

M. Zhang was supported by NSFC grant 11071234.

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Xiong, T., Shu, CW. & Zhang, M. WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows. J Sci Comput 53, 222–247 (2012). https://doi.org/10.1007/s10915-012-9578-7

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