  In this paper, a new five-point targeted essentially non-oscillatory (TENO)
scheme with adaptive dissipation is proposed. With the standard TENO weighting
strategy, the cut-off parameter $C_T$ determines the nonlinear numerical
dissipation of the resultant TENO scheme. Moreover, according to the
dissipation-adaptive TENO5-A scheme, the choice of the cut-off parameter $C_T$
highly depends on the effective scale sensor. However, the scale sensor in
TENO5-A can only roughly detect the discontinuity locations instead of
evaluating the local flow wavenumber as desired. In this work, a new five-point
scale sensor, which can estimate the local flow wavenumber accurately, is
proposed to further improve the performance of TENO5-A. In combination with a
hyperbolic tangent function, the new scale sensor is deployed to the TENO5-A
framework for adapting the cut-off parameter $C_T$, i.e., the local nonlinear
dissipation, according to the local flow wavenumber. Overall, sufficient
numerical dissipation is generated to capture discontinuities, whereas a
minimum amount of dissipation is delivered for better resolving the smooth
flows. A set of benchmark cases is simulated to demonstrate the performance of
the new TENO5-A scheme.
