Property-Preserving Data Compression for Incompressible Flows
We develop a method for lossy compression of incompressible (i.e., divergence-free) velocity fields that preserves zero divergence and, on periodic domains, periodicity. We fit the nodal velocities with property-preserving matrix-valued kernels and compress their coefficients using standard lossy compressors. Every decompressed coefficient vector defines a field with the same constraints, independently of the compression tolerance. We present several fitting schemes designed around either low-rank representation of or sparsity in the interpolation matrix. More specifically, we show results for global Matérn interpolation, a two-level Nyström approximation, Nyström--Wendland residual interpolation, multilevel Wendland interpolation and a property-preserving (redundant) kernel frame. We derive nodal error bounds that relate the compressor tolerance to the additional velocity error. Experiments with four compressors on cavity, Taylor--Green, and species-transport flows verify the bounds under their coefficient-error assumptions and compare storage at matched velocity accuracy. The low-rank methods give compact representations when they resolve the velocity field sufficiently accurately; residual, multilevel, and frame interpolation extend the attainable accuracy when they do not. We also measure changes in turbulent velocity statistics. The resulting representations support an accuracy--compression tradeoff while preserving incompressibility and periodicity analytically.