<ul><li>Accurately reconstructing continuous flow fields from sparse or indirect measurements remains an open challenge.</li><li>A novel flow field reconstruction framework based on divergence-free kernels (DFKs) is introduced.</li><li>DFKs-Wen4 (matrix-valued radial basis functions derived from Wendland's C^4 polynomial) are identified as the optimal form of analytically divergence-free approximation for velocity fields.</li><li>Experiments demonstrate that DFKs-Wen4 outperform other divergence-free representations in reconstruction accuracy and computational efficiency.</li></ul>

Representing Flow Fields with Divergence-Free Kernels for Reconstruction

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