An Improved Multi-Order Candidates Nonlinear Weighted Scheme with Smooth Scale-Adaptive Separation for Turbulence Simulations

High-order nonlinear shock capture schemes with low numerical dispersion and dissipation errors have significant advantages for simulations of compressible turbulent flows. However, the co-existence of flow discontinuities and multi-scale turbulence poses significant challenges for high-fidelity numerical simulations. Here, an improved six-point nonlinear interpolation is proposed that combines a generalized multi-order candidates (MOC) and adaptive smooth scale separation method. MOC framework extends the classical nonlinear weighting based on candidates of the same order to a weighted summation of the classical weighting results of different orders, improving the spectral properties. Based on MOC framework, a new smooth scale separation is proposed to make a smooth transition between resolved and non-resolved scales, which is free from the influence of the linear weights choice and has good performance in shock capturing. Furthermore, a new scale sensor is developed for evaluating the local flow wavenumber accurately to further enhance the performance of the adaptive dissipation control, denoted as MOC6-STA. Spectral analysis, benchmark cases and scale resolving turbulence simulations have been conducted to assess the proposed MOC-STA, which clearly show its advantage in stable shock-capturing and low dissipation in turbulence simulations.