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Volume 35, Issue 4
Finite-Volume TENO Scheme with a New Cell-Interface Flux Evaluation Strategy for Unstructured Meshes

Tian Liang & Lin Fu

Commun. Comput. Phys., 35 (2024), pp. 938-972.

Published online: 2024-05

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  • Abstract

The development of high-order shock-capturing schemes is critical for compressible fluid simulations, in particular for cases where both shock waves and small-scale turbulence structures present. As one of the state-of-the-art high-order numerical schemes, the family of high-order targeted ENO (TENO) schemes proposed by Fu et al. [Journal of Computational Physics 305 (2016): 333-359] has been demonstrated to perform well for compressible gas dynamics on structured meshes and recently extended to unstructured meshes by Ji et al. [Journal of Scientific Computing 92(2022): 1-39]. In this paper, with the observation that the TENO scheme not only provides the high-order reconstructed data at the cell interface but also features the potential to separate the local flow scales in the wavenumber space, we propose a low-dissipation finite-volume TENO scheme with a new cell-interface flux evaluation strategy for unstructured meshes. The novelty originates from the fact that the local flow scales are classified, following a strong scale separation in the reconstruction process, as “very smooth” or not. When the corresponding large central-biased stencil for the targeted cell interface is judged to be “very smooth”, a low-dissipation Riemann solver, even the non-dissipative central flux scheme, is employed for the cell-interface flux computing. Otherwise, a dissipative approximate Riemann solver is employed to avoid spurious oscillations and achieve stable shock-capturing. Such a strategy provides separate control over the numerical dissipation of the high-order reconstruction process and the cell-interface flux calculation within a unified framework and leads to a resultant finite-volume method with extremely low-dissipation properties and good numerical robustness. Without parameter tuning case by case, a set of canonical benchmark simulations has been conducted to assess the performance of the proposed scheme.

  • AMS Subject Headings

35L65, 65M08, 76J20, 76N15, 76F05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-35-938, author = {Liang , Tian and Fu , Lin}, title = {Finite-Volume TENO Scheme with a New Cell-Interface Flux Evaluation Strategy for Unstructured Meshes}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {4}, pages = {938--972}, abstract = {

The development of high-order shock-capturing schemes is critical for compressible fluid simulations, in particular for cases where both shock waves and small-scale turbulence structures present. As one of the state-of-the-art high-order numerical schemes, the family of high-order targeted ENO (TENO) schemes proposed by Fu et al. [Journal of Computational Physics 305 (2016): 333-359] has been demonstrated to perform well for compressible gas dynamics on structured meshes and recently extended to unstructured meshes by Ji et al. [Journal of Scientific Computing 92(2022): 1-39]. In this paper, with the observation that the TENO scheme not only provides the high-order reconstructed data at the cell interface but also features the potential to separate the local flow scales in the wavenumber space, we propose a low-dissipation finite-volume TENO scheme with a new cell-interface flux evaluation strategy for unstructured meshes. The novelty originates from the fact that the local flow scales are classified, following a strong scale separation in the reconstruction process, as “very smooth” or not. When the corresponding large central-biased stencil for the targeted cell interface is judged to be “very smooth”, a low-dissipation Riemann solver, even the non-dissipative central flux scheme, is employed for the cell-interface flux computing. Otherwise, a dissipative approximate Riemann solver is employed to avoid spurious oscillations and achieve stable shock-capturing. Such a strategy provides separate control over the numerical dissipation of the high-order reconstruction process and the cell-interface flux calculation within a unified framework and leads to a resultant finite-volume method with extremely low-dissipation properties and good numerical robustness. Without parameter tuning case by case, a set of canonical benchmark simulations has been conducted to assess the performance of the proposed scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0289}, url = {http://global-sci.org/intro/article_detail/cicp/23090.html} }
TY - JOUR T1 - Finite-Volume TENO Scheme with a New Cell-Interface Flux Evaluation Strategy for Unstructured Meshes AU - Liang , Tian AU - Fu , Lin JO - Communications in Computational Physics VL - 4 SP - 938 EP - 972 PY - 2024 DA - 2024/05 SN - 35 DO - http://doi.org/10.4208/cicp.OA-2023-0289 UR - https://global-sci.org/intro/article_detail/cicp/23090.html KW - TENO scheme, WENO scheme, high-order numerical scheme, unstructured mesh, low-dissipation scheme, compressible fluids. AB -

The development of high-order shock-capturing schemes is critical for compressible fluid simulations, in particular for cases where both shock waves and small-scale turbulence structures present. As one of the state-of-the-art high-order numerical schemes, the family of high-order targeted ENO (TENO) schemes proposed by Fu et al. [Journal of Computational Physics 305 (2016): 333-359] has been demonstrated to perform well for compressible gas dynamics on structured meshes and recently extended to unstructured meshes by Ji et al. [Journal of Scientific Computing 92(2022): 1-39]. In this paper, with the observation that the TENO scheme not only provides the high-order reconstructed data at the cell interface but also features the potential to separate the local flow scales in the wavenumber space, we propose a low-dissipation finite-volume TENO scheme with a new cell-interface flux evaluation strategy for unstructured meshes. The novelty originates from the fact that the local flow scales are classified, following a strong scale separation in the reconstruction process, as “very smooth” or not. When the corresponding large central-biased stencil for the targeted cell interface is judged to be “very smooth”, a low-dissipation Riemann solver, even the non-dissipative central flux scheme, is employed for the cell-interface flux computing. Otherwise, a dissipative approximate Riemann solver is employed to avoid spurious oscillations and achieve stable shock-capturing. Such a strategy provides separate control over the numerical dissipation of the high-order reconstruction process and the cell-interface flux calculation within a unified framework and leads to a resultant finite-volume method with extremely low-dissipation properties and good numerical robustness. Without parameter tuning case by case, a set of canonical benchmark simulations has been conducted to assess the performance of the proposed scheme.

Liang , Tian and Fu , Lin. (2024). Finite-Volume TENO Scheme with a New Cell-Interface Flux Evaluation Strategy for Unstructured Meshes. Communications in Computational Physics. 35 (4). 938-972. doi:10.4208/cicp.OA-2023-0289
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