A fifth-order low-dissipation discontinuity-resolving TENO scheme for compressible flow simulation

Abstract

For compressible flows characterized by a wide range of flow length scales and discontinuities, it is still an open challenge to design the optimal schemes, which resolve the small-scale flow structures with low numerical dissipation and capture the shock waves without artificial oscillations. In Takagi et al. [1], a novel TENO5-THINC scheme with the combination of classical TENO5 (fifth-order Targeted Essentially Non-Oscillatory) scheme and the non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) reconstruction has been proposed. Building upon the strategy of isolating discontinuities from smooth and high-wavenumber regions, in the present work, a new very low-dissipation TENO scheme with discontinuity-resolving property is proposed for compressible flow simulations based on three new concepts: (1) an improved discontinuity-detecting criterion is devised based on the TENO weighting strategy, which significantly enhances the discontinuity-detecting accuracy compared to that in TENO5-THINC; (2) A local interpolation-like strategy is proposed to represent the detected discontinuity with subcell resolutions, and this strategy can minimize the numerical dissipation even when compared to the THINC reconstruction scheme; (3) According to the varying sharpness of the discontinuities separated by the discontinuity-detecting indicator, the local interpolation-like strategy is extended with a two-steepness approximation. Specifically, the discontinuities will be classified as genuinely sharp discontinuities and general ones. For the genuinely sharp discontinuities, the interface flux will be estimated by a steeper step-like function with even less numerical dissipation. The resulting scheme maintains the high-order and low-dissipation properties of the TENO scheme for smooth flow scales, while further improving the discontinuity-resolving capability and suppressing the numerical oscillations in the vicinity of discontinuities. A variety of benchmark cases with broadband length scales as well as discontinuities is presented to demonstrate the high wave-resolution property and the sharp shock-capturing capability of the proposed scheme.