High-Order Low-Dissipation Shock-Resolving TENO-THINC Schemes for Hyperbolic Conservation Laws (Communications in Computational Physics, 2023)
While the recently proposed TENO (targeted essentially non-oscillatory)schemes [Fu et al., Journal of Computational Physics 305 (2016): 333-359] exhibit betterperformance than the classical WENO (weighted essentially non-oscillatory) schemeswith the same accuracy order, there is still a room for further improvement, e.g., thephysical discontinuities may be significantly smeared by the excessive numerical dissipation due to the enforcement of the ENO property after a long-time advection. Morerecently, a new fifth-order TENO5-THINC scheme is proposed by coupling the TENO5scheme with a non-polynomial THINC (tangent of hyperbola for interface capturing) scheme based on a parameter-free discontinuity indicator. The novelty originatesfrom the fact that the new strategy locates the discontinuities accurately and deploysthe jump-like THINC reconstruction scheme for resolving the discontinuities with asub-cell resolution, instead of enforcing the ENO property. The new scheme successfully leverages the excellent wave-resolution property of standard TENO schemes forsmooth 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 couplingstrategies. Without loss of generality, the six- and eight-point TENO-THINC schemesare 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 significantly lower numerical dissipation when compared to the counterpart TENOschemes without sacrificing numerical robustness. The presented numerical resultsrepresent the state-of-the-art in the literature and can serve as references for futurealgorithm development.