🤖 AI Summary
This work addresses the challenge of achieving both efficient compact representation and high physical fidelity in turbulent flow fields by proposing a continuous parameterization method based on learnable local Gaussian primitives. By superimposing anisotropic Gaussian kernels with adjustable positions, amplitudes, and scales, the approach enables a mesh-free, compact representation that supports accurate computation of derived quantities such as vorticity. The incorporation of a multi-resolution architecture and compactly supported Beta basis functions further enhances geometric expressiveness. In the Taylor–Green vortex benchmark, the method achieves compression ratios of 10³–10⁴ while preserving high-fidelity velocity fields, effectively recovering mid- to high-frequency structures and mitigating vorticity dissipation. These results indicate that geometric representational capacity—not merely parameter count—is the key limiting factor, laying the groundwork for structure-aware, physics-informed flow field compression.
📝 Abstract
Representing turbulent flow fields in a compact yet physically faithful form remains a central challenge in computational fluid dynamics. We propose a continuous parametric representation based on localized Gaussian primitives, in which the velocity field is modeled as a superposition of kernels with learnable positions, amplitudes, and scales. This formulation yields a compact, grid-independent encoding while enabling evaluation of derived quantities such as vorticity and enstrophy. The approach is assessed on three-dimensional Taylor-Green vortex fields spanning stages from smooth flow to fully developed turbulence. We quantify the compression-accuracy trade-off using both primary variables and derivative-sensitive diagnostics. The baseline isotropic formulation achieves high velocity accuracy at compression ratios exceeding 1e3-1e4, but exhibits substantial enstrophy degradation due to loss of small-scale structure. To address this limitation, we investigate structure-aware extensions including adaptive placement, multi-resolution kernels, and anisotropic Gaussians. The anisotropic formulation provides the most consistent improvement, better aligning with elongated vortical structures and recovering intermediate- and high-wavenumber content, while other strategies yield modest gains. A compact-support Beta basis improves enstrophy in some cases but introduces localized artifacts. Overall, the results indicate that the main limitation of baseline Gaussian representations lies in geometric expressiveness rather than parameter count. The proposed framework provides a compact, interpretable, and continuous representation of turbulent flows, and establishes a foundation for structure-aware and physics-informed flow compression.