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High-Order Finite-Volume TENO Schemes with Dual ENO-Like Stencil Selection for Unstructured Meshes

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Abstract

The TENO-family schemes (Fu et al. in J Comput Phys 305: 333–359, 2016) have been demonstrated to perform well for compressible gas dynamics and turbulent flow predictions on structured meshes. However, the extension of the TENO schemes to unstructured meshes is non-trivial and challenging, particularly when the multiple design objectives are pursued simultaneously, i.e., restoring the high-order accuracy in smooth regions, retaining the low numerical dissipation for small-scale features, maintaining the sharp shock-capturing property, and featuring the good numerical robustness for high-Mach flows. In this work, a family of very-high-order (up to seventh-order accuracy) robust finite-volume TENO schemes with dual ENO-like stencil selection for unstructured meshes is proposed. The stencils include one large stencil and several small stencils. The novelty originates from a so-called dual ENO-like stencil selection strategy. Following a strong scale separation, the ENO-like stencil selection procedure with a small \(C_T\) is first enforced among all the candidates such that the high-order candidate scheme on the large stencil is adopted for the final reconstruction when the local flow is smooth. If the large stencil is judged to be crossed by discontinuities, a second ENO-like stencil selection with a relatively large \(C_T\) is applied to all the left small stencils and the ENO property is obtained by selecting the smooth small stencils which are not crossed by discontinuities. The smaller \(C_T\) in the first stage ensures that the high-order reconstruction is restored for smooth flow scales with higher wavenumbers. On the other hand, the larger \(C_T\) in the second stage can enforce a strong nonlinear adaptation for capturing discontinuities with better robustness. Such a dual ENO-like stencil selection strategy introduces an explicit scale separation and deploys the optimal strategy for different types of flows correspondingly. Without parameter tuning, a set of benchmark simulations has been conducted to validate the performance of the proposed TENO schemes. Numerical results demonstrate the good numerical robustness and the low-dissipation property for highly compressible flows with shockwaves.

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Funding

Z.J. is supported by the Fundamental Research Funds for the Central Universities (No. D5000210971), Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515110314), and the General Program of Taicang Basic Research Project (No. TC2022JC07). L.F. acknowledges the fund from the Research Grants Council (RGC) of the Government of Hong Kong Special Administrative Region (HKSAR) with RGC/ECS Project (No. 26200222), the fund from Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515011779), and the fund from the Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone (No. HZQB-KCZYB-2020083).

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Authors and Affiliations

  1. School of Software, Northwestern Polytechnical University, Xi’an, 710072, 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. HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute, Futian, Shenzhen, China

    Lin Fu

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Ji, Z., Liang, T. & Fu, L. High-Order Finite-Volume TENO Schemes with Dual ENO-Like Stencil Selection for Unstructured Meshes. J Sci Comput 95, 76 (2023). https://doi.org/10.1007/s10915-023-02199-1

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