Abstract
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.
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