| Data storage issues pose a potential problem in the performance and analysis of turbulence simulations. One tool that has successfully addressed such performance problems in other domains is data compression. Unfortunately, data from turbulence simulations does not usefully compress with lossless methods. This has led to the examination of wavelet-based lossy coding techniques for compressing turbulence data. One of the key issues is that a significant portion of work on lossy coding involves image coding. The error measures used in image coding are not meaningful in the physical context of turbulence data. For this work with turbulence data, error is measured relative to standard deviation and (for significant values) also as relative error. Depending on the quantities of interest and the evaluation criteria, it is found that compression ratios from 4:1 to 256:1 are achievable in the wavelet-based lossy coding of turbulence data.; Studies of wavelet-packet-based coding found that finding a best-basis is sufficiently complex that in performance-critical applications, wavelet-packet-based coding is not beneficial. The experiments with wavelet packets and varying the bit allocation have demonstrated the need for cost functions that better match the relevant error in quantities of interest.; In addition to varying the bit allocation among subbands, other experiments altering the coding process were conducted. Some, such as using non-uniform quantization, raise issues for further study, while others are at best of limited usefulness.; Examination of wavelet-subband statistics has demonstrated the differences between turbulence data and images. Depending on the view one takes, the statistical characteristics point to the need to use either thresholding or non-uniform quantization as part of the coding process. Disappointing experiments with region-of-interest coding suggest that the correct choice is non-uniform quantization.; A mapping between pruned tree-structured scalar quantizers, a form of scalar non-uniform successive refinement quantizer, and piecewise linear companding is described. This mapping provides the potential for alternative design strategies for this class of quantizers. In particular, it provides a sub-optimal design method for these quantizers. |
