@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0289},
url = {http://global-sci.org/intro/article_detail/cicp/23090.html}
}