A novel Wavelet-based adaptive Delayed Detached Eddy Simulation (W-DDES) approach for simulations of wall-bounded compressible turbulent flows is proposed. The new approach utilizes anisotropic wavelet-based mesh refinement and its effectiveness is demonstrated for flow simulations using the Spalart-Allmaras DDES model. A variable wavelet thresholding strategy blending two distinct thresholds for the Reynolds-averaged Navier-Stokes (RANS) and Large-Eddy Simulation (LES) regimes is used. A novel mesh adaptation on mean and fluctuation quantities with different wavelet threshold levels is proposed. The new strategy is more accurate and efficient compared to the adaptation on instantaneous quantities using a priori defined uniform thresholds. The effectiveness of the W-DDES method is demonstrated by comparing the results of the W-DDES simulations with results already available in the literature. A supersonic plane channel flow is tested as a benchmark wall-bounded flow. Both the accuracy indicated by the threshold and efficiency in terms of degrees of freedom for the novel adaptation strategy are successfully gained compared with the wavelet-based adaptive LES method. Moreover, the newly proposed W-DDES resolves the typical log-layer match issue encountered in the conventional non-adaptive DDES method mainly due to the use of wavelet-based adaptive mesh refinement. The current study serves as a crucial step towards construction of a unified wavelet-based adaptive hierarchical RANS/LES modeling framework, capable of performing simulations of varying fidelities from no-modeling direct numerical simulations to full-modeling RANS simulations.
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