Towards an adaptive wavelet-based 3D Navier-Stokes Solver

In this paper we present results obtained using wavelet methods for the analysis and simulation of two-dimensional turbulence, and a preliminary study of a three-dimensional turbulent channel flow. The two-dimensional results show the efficiency of wavelets for the numerical simulation of turbulence, and suggest new methods for modelling the flow, based on a decomposition into coherent and incoherent parts. The three-dimensional study compares different wavelet type approaches applied to instantaneous velocity, vorticity and pressure fields. At least for the data and the setting considered in our experiments, i.e. flows with dominating boundary layer, the results indicate which of the various forms of the three-dimensional Navier-Stokes Equations (3D-NSE) (primitive variables, vorticity-streamfunction formulation) and which multiscale approach is well suited for the numerical integration of the 3D-NSE. In addition, we present efficient techniques for the implementation and parallelization of an adaptive wavelet-based 3D-NSE solver.