A Targeted ENO Scheme as Implicit Model for Turbulent and Genuine Subgrid Scales (Communications in Computational Physics, 2019)
Even for state-of-the-art implicit LES (ILES) methods, where the truncationerror acts as physically-motivated subgrid-scale model, simultaneously resolving turbulent and genuine non-turbulent subgrid scales is an open challenge. For the purposeof dealing with non-turbulent subgrid scales, such as shocks, extra sensors, which often are case-dependent, are generally employed. The problem originates in the lack ofscale-separation between low-wavenumber resolved-scale regions, high-wavenumberresolved or non-resolved fluctuations, and discontinuities. The targeted ENO (TENO)approach allows for separately designing the dispersive and dissipative truncationerror components. Thus it provides a suitable environment to develop an implicitLES model. In this paper, we extend previous work and propose a variant of TENOfamily scheme [Fu et al., JCP 305 (2016): 333-359], which can separate resolved andnonresolved scales effectively. The novel idea is to propose a nonlinear dissipation-control strategy by adapting the cut-off parameter CT dynamically while measuringthe nonsmoothness based on the first-order undivided difference. Low-wavenumbersmooth scales are handled by an optimized linear scheme while high-wavenumbercomponents, that involve nonresolved fluctuations and discontinuities, are subjectedto adaptive nonlinear dissipation. A set of benchmark simulations with a wide range oflength-scales and with discontinuities has been conducted without specific parameteradaptation. Numerical experiments demonstrate that the proposed TENO8-A schemeexhibits robust shock-capturing and high wave-resolution properties, and that it issuitable for simulating flow fields that contain isotropic turbulence and shocks. It is apromising alternative to other viable approaches.