@Article{CiCP-34-4,
author = {Takagi, Shinichi and Wakimura, Hiro and Lin, Fu and Xiao, Feng},
title = {High-Order Low-Dissipation Shock-Resolving TENO-THINC Schemes for Hyperbolic Conservation Laws},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {4},
pages = {1043--1078},
abstract = {<p style="text-align: justify;">While the recently proposed TENO (targeted essentially non-oscillatory)
schemes [Fu et al., Journal of Computational Physics 305 (2016): 333-359] exhibit better
performance than the classical WENO (weighted essentially non-oscillatory) schemes
with the same accuracy order, there is still a room for further improvement, e.g., the
physical discontinuities may be significantly smeared by the excessive numerical dissipation due to the enforcement of the ENO property after a long-time advection. More
recently, a new fifth-order TENO5-THINC scheme is proposed by coupling the TENO5
scheme with a non-polynomial THINC (tangent of hyperbola for interface capturing) scheme based on a parameter-free discontinuity indicator. The novelty originates
from the fact that the new strategy locates the discontinuities accurately and deploys
the jump-like THINC reconstruction scheme for resolving the discontinuities with a
sub-cell resolution, instead of enforcing the ENO property. The new scheme successfully leverages the excellent wave-resolution property of standard TENO schemes for
smooth and under-resolved continuous scales and the discontinuity-resolving capability of THINC for reconstructing genuine discontinuities. In this work, we further develop the low-dissipation discontinuity-resolving very-high-order TENO-THINC reconstruction schemes for hyperbolic conservation laws by proposing tailored coupling
strategies. Without loss of generality, the six- and eight-point TENO-THINC schemes
are developed, and the explicit formulas are given as well as the built-in parameters.
Based on a set of critical benchmark simulations, the newly proposed schemes show&nbsp;significantly lower numerical dissipation when compared to the counterpart TENO
schemes without sacrificing numerical robustness. The presented numerical results
represent the state-of-the-art in the literature and can serve as references for future
algorithm development.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0061},
url = {https://global-sci.com/article/79389/high-order-low-dissipation-shock-resolving-teno-thinc-schemes-for-hyperbolic-conservation-laws}
}