A Scale-Adaptive TENO Scheme based on a New Smoothness Indicator

This work presents a new smoothness indicator for the Targeted Essentially Non-Oscillatory (TENO) scheme based on the generalized undivided difference method. Furthermore, to prevent excessive numerical dissipation in the low and intermediate wavenumbers, the threshold regulating parameter in the standard TENO scheme is changed to correspond to the local effective scaled wavenumber. A considerable improvement in spectral property is observed using approximate dispersion relation (ADR) techniques. A set of numerical test cases involving both discontinuities and small-scale structures demonstrate that the current systems can capture more scales with less dissipation than the original TENO scheme. These approaches also promise additional higher-order advances in the future.