Property-Preserving Data Compression for Incompressible Flows
Abstract
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.
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BibTeX
@misc{pluzhnik2026propertypreserving,
title = {{Property-Preserving Data Compression for Incompressible Flows}},
author = {Andrey Pluzhnik and Ramansh Sharma and Martin Burtscher and Varun Shankar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02776},
eprint = {2610.02776},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02776},
}
RIS
TY - UNPB
TI - Property-Preserving Data Compression for Incompressible Flows
AU - Andrey Pluzhnik
AU - Ramansh Sharma
AU - Martin Burtscher
AU - Varun Shankar
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02776
UR - https://arxiv.org/abs/2610.02776
AB - 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.
ER -