Improved five- And six-point targeted essentially nonoscillatory schemes with adaptive dissipation

This Paper proposes an improvement of the five- and six-point targeted essentially nonoscillatory (TENO5 and TENO6) schemes by introducing an adaptive dissipation-control strategy. Nonlinear numerical dissipation is controlled by dynamically adjusting the cutoff parameter in the TENO weighting strategy according to the first-order smoothness measure of the local flow scales. For the five-point reconstruction, the dissipation bandwidth of the underlying linear scheme is delayed by introducing slight antidissipation at low wave numbers with small dispersion errors. A new sixth-order scale-separation parameter τ₅ is derived, and the modified TENO5-A scheme is third-order accurate. For the six-point reconstruction, the dispersion and dissipation errors are optimized separately, resulting in a modified fourth-order TENO6-A scheme. All necessary parameters are determined by spectral analyses and are shown to be problem independent by numerical experiments. A set of benchmark cases, including highly compressible gas dynamics and nearly incompressible and compressible turbulence decay, is considered. Numerical experiments demonstrate that both the proposed TENO5-A and TENO6-A schemes show excellent performance for shocks and broadband turbulence. The turbulence statistics obtained with TENO6-A at coarse resolution are comparable to those from the state-of-the-art implicit large-eddy simulation model and agree well with direct numerical simulation data.