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A Robust Reconstruction for Unstructured WENO Schemes

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Abstract

The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order numerical methods for hyperbolic partial differential equations (PDEs). While WENO schemes on structured meshes are quite mature, the development of finite volume WENO schemes on unstructured meshes is more difficult. A major difficulty is how to design a robust WENO reconstruction procedure to deal with distorted local mesh geometries or degenerate cases when the mesh quality varies for complex domain geometry. In this paper, we combine two different WENO reconstruction approaches to achieve a robust unstructured finite volume WENO reconstruction on complex mesh geometries. Numerical examples including both scalar and system cases are given to demonstrate stability and accuracy of the scheme.

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Acknowledgements

This research was supported by NSF grant DMS-0810413.

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Authors and Affiliations

  1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Yuan Liu & Yong-Tao Zhang

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  1. Yuan Liu
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  2. Yong-Tao Zhang
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Correspondence to Yong-Tao Zhang.

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Liu, Y., Zhang, YT. A Robust Reconstruction for Unstructured WENO Schemes. J Sci Comput 54, 603–621 (2013). https://doi.org/10.1007/s10915-012-9598-3

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  • DOI: https://doi.org/10.1007/s10915-012-9598-3

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