Survey and analysis of multiresolution methods for turbulence data

• We survey various multi-resolution geometric methods for turbulence representation.
• The flow contains novel aspects, not examined before, like variable density.
• The ability to preserve flow properties with reduced set of coefficients is examined.
• An extensive list of recommendations for the best decomposition algorithms is given.
• The cubic B-spline wavelets provide the best tradeoffs in efficiency versus accuracy.

This paper compares the effectiveness of various multi-resolution geometric representation methods, such as B-spline, Daubechies, Coiflet and Dual-tree wavelets, curvelets and surfacelets, to capture the structure of fully developed turbulence using a truncated set of coefficients. The turbulence dataset is obtained from a Direct Numerical Simulation of buoyancy driven turbulence on a 5123 mesh size, with an Atwood number, A=0.05,A=0.05,and turbulent Reynolds number, Ret=1800,Ret=1800,and the methods are tested against quantities pertaining to both velocities and active scalar (density) fields and their derivatives, spectra, and the properties of constant density surfaces. The comparisons between the algorithms are given in terms of performance, accuracy, and compression properties. The results should provide useful information for multi-resolution analysis of turbulence, coherent feature extraction, compression for large datasets handling, as well as simulations algorithms based on multi-resolution methods. The final section provides recommendations for best decomposition algorithms based on several metrics related to computational efficiency and preservation of turbulence properties using a reduced set of coefficients.