Finite-Volume TENO Scheme with a New Cell-Interface Flux Evaluation Strategy for Unstructured Meshes
Year: 2024
Author: Tian Liang, Lin Fu
Communications in Computational Physics, Vol. 35 (2024), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0289
Communications in Computational Physics, Vol. 35 (2024), Iss. 4 : pp. 938–972
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: TENO scheme WENO scheme high-order numerical scheme unstructured mesh low-dissipation scheme compressible fluids.
Author Details
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New finite volume unstructured modified MR-WENO schemes for hyperbolic conservation laws
Zuo, Huimin
Zhu, Jun
Journal of Computational Physics, Vol. 523 (2025), Iss. P.113672
https://doi.org/10.1016/j.jcp.2024.113672 [Citations: 1]