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A Class of New High-order Finite-Volume TENO Schemes for Hyperbolic Conservation Laws with Unstructured Meshes

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Abstract

The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305(2016): 333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy, the low numerical dissipation, and the sharp shock-capturing capability. However, the applications are still restricted to simple geometries with Cartesian or curvilinear meshes. In this work, a new class of high-order shock-capturing TENO schemes for unstructured meshes are proposed. Similar to the standard TENO schemes and some variants of WENO schemes, the candidate stencils include one large stencil and several small third-order stencils. Following a strong scale-separation procedure, a tailored novel ENO-like stencil selection strategy is proposed such that the high-order accuracy is restored in smooth regions by selecting the candidate reconstruction on the large stencil while the ENO property is enforced near discontinuities by adopting the candidate reconstruction from smooth small stencils. The nonsmooth stencils containing genuine discontinuities are explicitly excluded from the final reconstruction, leading to excellent numerical stability. Different from the WENO concept, such unique sharp stencil selection retains the low numerical dissipation without sacrificing the shock-capturing capability. The newly proposed framework enables arbitrarily high-order TENO reconstructions on unstructured meshes. For conceptual verification, the TENO schemes with third- to sixth-order accuracy are constructed. Without parameter tuning case by case, the performance of the proposed TENO schemes is demonstrated by examining a set of benchmark cases with broadband flow length scales.

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Data Availability

The data that support the findings of this study are available on request from the corresponding author, Lin Fu.

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Funding

Lin Fu acknowledges the fund from Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515011779) and the fund from Key Laboratory of Computational Aerodynamics, AVIC Aerodynamics Research Institute.

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Authors and Affiliations

  1. School of Software, Northwestern Polytechnical University, Taicang, Jiangsu, China

    Zhe Ji

  2. Yangtze River Delta Research Institute of NPU, Taicang, Jiangsu, China

    Zhe Ji

  3. Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Tian Liang & Lin Fu

  4. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Lin Fu

  5. Center for Ocean Research in Hong Kong and Macau (CORE), The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Lin Fu

  6. Shenzhen Research Institute, The Hong Kong University of Science and Technology, Shenzhen, China

    Lin Fu

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  1. Zhe Ji
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Ji, Z., Liang, T. & Fu, L. A Class of New High-order Finite-Volume TENO Schemes for Hyperbolic Conservation Laws with Unstructured Meshes. J Sci Comput 92, 61 (2022). https://doi.org/10.1007/s10915-022-01925-5

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