A Targeted ENO Scheme as Implicit Model for Turbulent and Genuine Subgrid Scales

Even for state-of-the-art implicit LES (ILES) methods, where the truncation error acts as physically-motivated subgrid-scale model, simultaneously resolving turbulent and genuine non-turbulent subgrid scales is an open challenge. For the purpose of 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 of scale-separation between low-wavenumber resolved-scale regions, high-wavenumber resolved or non-resolved fluctuations, and discontinuities. The targeted ENO (TENO) approach allows for separately designing the dispersive and dissipative truncation error components. Thus it provides a suitable environment to develop an implicit LES model. In this paper, we extend previous work and propose a variant of TENO family scheme [Fu et al., JCP 305 (2016): 333-359], which can separate resolved and nonresolved scales effectively. The novel idea is to propose a nonlinear dissipation-control strategy by adapting the cut-off parameter C-T dynamically while measuring the nonsmoothness based on the first-order undivided difference. Low-wavenumber smooth scales are handled by an optimized linear scheme while high-wavenumber components, that involve nonresolved fluctuations and discontinuities, are subjected to adaptive nonlinear dissipation. A set of benchmark simulations with a wide range of length-scales and with discontinuities has been conducted without specific parameter adaptation. Numerical experiments demonstrate that the proposed TENO8-A scheme exhibits robust shock-capturing and high wave-resolution properties, and that it is suitable for simulating flow fields that contain isotropic turbulence and shocks. It is a promising alternative to other viable approaches.