A fully adaptive wavelet-based approach to homogeneous turbulence simulation

The ability of wavelet multi-resolution analysis to detect and track the energy-containing motions that govern the dynamics of a fluid flow offers a unique hierarchical framework for modelling and simulating turbulence. In this paper, the role of the wavelet thresholding level in wavelet-based modelling and simulation of turbulent flows is systematically examined. The thresholding level controls the relative importance of resolved energetic structures and residual unresolved background flow and, thus, the achieved turbulence resolution. A fully adaptive eddy capturing approach is developed that allows variable-fidelity numerical simulations of turbulence to be performed. The new method is based on wavelet filtering with time-varying thresholding. The thresholding level automatically adapts to the desired turbulence resolution during the simulation. The filtered governing equations supplemented by a localized dynamic energy-based closure model are solved numerically using the adaptive wavelet collocation method. The approach is successfully tested in the numerical simulation of both linearly forced and freely decaying homogeneous turbulence.