Wavelet-Based Adaptive Unsteady Reynolds-Averaged Navier-Stokes Simulations of Wall-Bounded Compressible Turbulent Flows

A wavelet-based adaptive approach, called wavelet-based adaptive unsteady Reynolds-averaged Navier-Stokes (WA-URANS), is proposed to solve the URANS equations for the computation of wall-bounded internal and external compressible turbulent flows. The new approach uses anisotropic wavelet-based mesh refinement, and its effectiveness is demonstrated for flow simulations with two different turbulence models, namely, the Spalart-Allmaras and k-omega models for a variety of two- and three-dimensional flow configurations with arbitrary geometries, different speed regimes, and various boundary conditions. Supersonic plane channel flow, a weakly compressible channel flow with periodic hill constrictions, a subsonic zero-pressure-gradient flat-plate boundary-layer flow, the separated flow over NASA wall-mounted hump, the Bachalo-Johnson flow (axisymmetric transonic bump flow), and a flow past a circular cylinder at a subcritical Reynolds number are tested as benchmark flows. The effectiveness and efficiency of the new wavelet-based approach are demonstrated by comparing the results of the WA-URANS simulations with literature data. This comprehensive validation of the WA-URANS approach encourages its application to practical problems of industrial interest, and demonstrates the feasibility of extending this approach to wavelet-based wall-modeled large-eddy simulation (LES) and hybrid URANS/LES. Finally, the current study serves as a baseline for the development of a unified hierarchical framework for eddy-resolving turbulence modeling, capable of performing computations of different fidelity, ranging from adaptive direct numerical simulations to adaptive URANS computations.