Wavelet-Based Adaptive Wall-Modeled Large Eddy Simulation Method For Compressible Turbulent Flows

A wavelet-based adaptive wall-modeled large eddy simulation (WA-WMLES) method is proposed for simulations of wall-bounded compressible turbulent flows. The approach utilizes the wavelet-based adaptive large eddy simulation (WA-LES), incorporated into the anisotropic-adaptive wavelet collocation method, to resolve the outer region of turbulent boundary layer, while the inner part is approximated by the equilibrium wall-shear-stress model. Such an approach for modeling the inner layer is crucial for wavelet-based adaptive turbulent flow simulations because the mesh resolution requirement for WA-LES to resolve inner viscous sublayer becomes computationally prohibitively expensive as the Reynolds number increases. In the outer layer region WA-LES computations take advantage of the wavelet-based local mesh refinement, which not only efficiently captures the physical characteristics of flows on a nearly optimal adaptive computational mesh, e.g., massive boundary layer separation, but also actively controls the error of the solution using a priori defined wavelet filtering threshold. A flat plate turbulent boundary layer flow and a separated flow over NASA's wall-mounted hump are tested to verify and validate the WA-WMLES approach. Good agreement of the results predicted by the WA-WMLES method is achieved compared to the reference data from experiments and simulations. The finest effective mesh resolution of the WA-WMLES is consistently higher than the one used in the wall-modeled LES (WMLES) found in literature, but comparable to the wall-resolved LES, while the similar accuracy is achieved with considerably fewer degrees of freedom than in nonadaptive WMLES. These observations demonstrate both accuracy and efficiency of the WA-WMLES method.