  The scale-resolving simulation of high speed compressible flow through direct
numerical simulation (DNS) or large eddy simulation (LES) requires
shock-capturing schemes to be more accurate for resolving broadband turbulence
and robust for capturing strong shock waves. In this work, we develop a new
paradigm of dissipation-controllable, shock capturing scheme to resolve
multi-scale flow structures in high speed compressible flow. This novel
paradigm of shock-capturing scheme is named as PnTm-BVD-CD. The proposed
PnTm-BVD-CD scheme has following desirable properties. First, it can capture
large-scale discontinuous structures such as strong shock waves without obvious
non-physical oscillations while resolving sharp contact, material interface and
shear layer. Secondly, the numerical dissipation property of PnTm-BVD-CD can be
effectively controlled between n+1 order upwind-biased scheme and
non-dissipative n+2 order central scheme through a simple tunable parameter
$\lambda$. Thirdly, with $\lambda=0.5$ the scheme can recover to n+2 order
non-dissipative central interpolation for smooth solution over all wavenumber,
which is preferable for solving small-scale structures in DNS as well as
resolvable-scale in explicit LES. Finally, the under-resolved small-scale can
be solved with dissipation controllable algorithm through so-called implicit
LES (ILES) approach.
