  High fidelity numerical simulation of compressible flow requires the
numerical method being used to have both stable shock-capturing capability and
high spectral resolution. Recently, a family of Targeted Essentially
Non-Oscillatory (TENO) schemes are developed to fulfill such requirements.
Although TENO has very low dissipation for smooth flow, it introduces a cutoff
value $C_T$ to maintain the non-oscillatory shock-capturing property. $C_T$ is
problem depended and therefore needs adjustments by trial and error for
different problems. As $C_T$ actually controls the dissipation property of
TENO, the choice of $C_T$ for better shock-capturing capability always means
higher dissipation. To overcome this, in this paper, a local adaptive method is
proposed for the choice of $C_T$. By introducing a novel adaptive function
based on the WENO smoothness indicators, $C_T$ is dynamically adjusted form
$1.0 \times 10.0^{-10}$ for lower dissipation to $1.0 \times 10.0^{-4}$ for
better capturing of shock according to the smoothness of the reconstruction
stencil. Numerical results of the new method are compared with those of the
original TENO method and the TENO-A method (Fu et al., JCP, 2017). It reveals
that the new method is capable of better suppressing numerical oscillations
near discontinuities while maintaining the low dissipation property of TENO at
lower extra computational cost.
