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The scale-resolving simulation of high speed compressible flow through directnumerical simulation (DNS) or large eddy simulation (LES) requiresshock-capturing schemes to be more accurate for resolving broadband turbulenceand robust for capturing strong shock waves. In this work, we develop a newparadigm of dissipation-controllable, shock capturing scheme to resolvemulti-scale flow structures in high speed compressible flow. This novelparadigm of shock-capturing scheme is named as PnTm-BVD-CD. The proposedPnTm-BVD-CD scheme has following desirable properties. First, it can capturelarge-scale discontinuous structures such as strong shock waves without obviousnon-physical oscillations while resolving sharp contact, material interface andshear layer. Secondly, the numerical dissipation property of PnTm-BVD-CD can beeffectively controlled between n+1 order upwind-biased scheme andnon-dissipative n+2 order central scheme through a simple tunable parameter$\lambda$. Thirdly, with $\lambda=0.5$ the scheme can recover to n+2 ordernon-dissipative central interpolation for smooth solution over all wavenumber,which is preferable for solving small-scale structures in DNS as well asresolvable-scale in explicit LES. Finally, the under-resolved small-scale canbe solved with dissipation controllable algorithm through so-called implicitLES (ILES) approach.

A new paradigm of dissipation-controllable, multi-scale resolving schemes for compressible flows