  In this work, a framework to construct arbitrarily high-order low-dissipation
shock-capturing schemes with flexible and controllable nonlinear dissipation
for convection-dominated problems is proposed. While a set of candidate
stencils of incremental width is constructed, each one is indicated as smooth
or nonsmooth by the ENO-like stencil selection procedure proposed in the
targeted essentially non-oscillatory (TENO) scheme [Fu et al., Journal of
Computational Physics 305 (2016): 333-359]. Rather than being discarded
directly as with TENO schemes, the nonsmooth candidates are filtered by an
extra nonlinear limiter, such as a monotonicity-preserving (MP) limiter or a
total variation diminishing (TVD) limiter. Consequently, high-order
reconstruction is achieved by assembling candidate fluxes with optimal linear
weights since they are either smooth reconstructions or filtered ones which
feature good non-oscillation property. A weight renormalization procedure as
with the standard TENO paradigm is not necessary. This new framework
concatenates the concepts of TENO, WENO and other nonlinear limiters for
shock-capturing, and provides a new insight to designing low-dissipation
nonlinear schemes. Through the adaptation of nonlinear limiters, nonlinear
dissipation in the newly proposed framework can be controlled separately
without affecting the performance in smooth regions. Based on the proposed
framework, a family of new six- and eight-point nonlinear schemes with
controllable dissipation is proposed. A set of critical benchmark cases
involving strong discontinuities and broadband fluctuations is simulated.
Numerical results reveal that the proposed new schemes capture discontinuities
sharply and resolve the high-wavenumber fluctuations with low dissipation,
while maintaining the desired accuracy order in smooth regions.
