A very-high-order TENO scheme for all-speed gas dynamics and turbulence

In this paper, we propose a new scale-separation formula and develop a very-high-order targeted ENO scheme, which shows exceptional performance in conventional compressible gas dynamics, high Mach-number simulations with vacuum or near-vacuum region, incompressible and compressible turbulence prediction. The modified TENO weighting strategy can be extended to arbitrarily very high-order reconstruction in a straightforward manner. The proposed 10-point TENO10-A scheme is optimized to satisfy an approximate-dispersion relation while maintaining the 8th-order accuracy in smooth regions. For conventional gas dynamics at low to moderate Mach numbers, the TENO10-A scheme is robust, and shows low numerical dissipation in resolving small-scale physical fluctuations while capturing the sharp discontinuities. For high-Mach number simulations, TENO10-A is numerically stable and preserves the ENO property with the assistance of a positivity-preserving flux limiter. In terms of turbulent flows, TENO10-A faithfully predicts energy transfer, and resolves vorticity, entropy and acoustic modal fluctuations. A set of benchmark simulations is considered to assess the performance of proposed scheme. (C) 2019 Elsevier B.V. All rights reserved.