发表机构
University of Utah; Texas State University（犹他大学; 德克萨斯州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种保持不可压缩流动散度为零和周期性的损压缩方法，通过属性保持核拟合与系数压缩，实现精度与压缩的权衡，并在多种流动上验证误差界。
AI 中文摘要
我们开发了一种针对不可压缩（即散度为零）速度场的损压缩方法，该方法保持零散度，并在周期域上保持周期性。我们使用属性保持的矩阵值核拟合节点速度，并使用标准损压缩器压缩其系数。每个解压后的系数向量定义了一个具有相同约束的场，与压缩容差无关。我们提出了几种拟合方案，这些方案围绕插值矩阵的低秩表示或稀疏性设计。具体而言，我们展示了全局Matérn插值、两级Nyström近似、Nyström-Wendland残差插值、多级Wendland插值以及属性保持（冗余）核框架的结果。我们推导了节点误差界，将压缩器容差与额外的速度误差联系起来。在空腔、Taylor-Green和物种输运流动上使用四种压缩器进行的实验验证了这些界在其系数误差假设下的有效性，并比较了在匹配速度精度下的存储量。低秩方法在足够准确地解析速度场时提供紧凑表示；残差、多级和框架插值在低秩方法不足时扩展了可达到的精度。我们还测量了湍流速度统计的变化。所得表示支持精度-压缩权衡，同时解析地保持不可压缩性和周期性。
英文摘要
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.
