A finite difference scale-adaptive TENO scheme for turbulence simulations

The classic finite difference shock-capturing methods, such as the WENO-JS scheme, are currently perceived as having limited small-scale capture capabilities due to excessive dissipation. A typical technique for enhancing the performance of a scheme in higher wavenumber regions is spectrum optimization. However, this approach compromises accuracy since it requires degrees of freedom to optimize dispersion and dissipation characteristics. In order to maintain accuracy while simultaneously enhancing spectral properties and significantly raising the maximum resolved bandwidth of a scheme, this study proposes a piecewise spectrum optimization method (PSOM) that employs schemes with different dispersion and dissipation properties in different wavenumber regions. A new scale sensor with improved resolving efficiency and more stable performance is developed to detect local wavenumbers more precisely after thoroughly investigating the scale sensor algorithm. The above method is applied to the 6th-order TENO scheme that can completely distinguish between discontinuous and smooth regions, the threshold value C_T is redesigned in different wavenumber regions to meet the dissipation requirements in various scale spaces, and a scale-adaptive scheme called TENO-SA is proposed. The potential advantages of the TENO-SA scheme in terms of spectral properties are demonstrated through the ADR and NSA methods. The accuracy analysis also indicates that the scheme can maintain optimal accuracy at low wavenumber regions. Numerous multi-scale benchmarks are introduced to validate the effectiveness of the PSOM and the new scale sensor, as well as the more effective and accurate simulation ability of the TENO-SA scheme for small-scale structures in broadband problems.