Wavelet-based adaptive large-eddy simulation of supersonic channel flow

The wavelet-based adaptive large-eddy simulation method is extended for computational modelling of compressible wall-bounded attached turbulent flows. The wavelet-threshold filtered compressible Navier–Stokes equations are derived. The unclosed terms in the governing equations are approximated by using eddy-viscosity and eddy-conductivity modelling procedures based on the anisotropic minimum-dissipation approach. The proposed filtering procedure is integrated with the adaptive anisotropic wavelet collocation method, which allows for the appropriate mesh stretching in the wall-normal direction. The performance of the method is assessed by conducting adaptive numerical simulations of fully developed supersonic flow in a plane channel with isothermal walls, which represents a well-established benchmark for wall-bounded turbulent compressible flows. The present results demonstrate both the feasibility and the effectiveness of the novel wavelet-based adaptive method in the high-speed compressible regime, showing good agreement with reference numerical solutions.