Large-scale multiscale simulations in fluid dynamics increasingly rely on complex geometries, adaptive refinement, and coupled physics, producing spatiotemporal fields whose storage and movement can dominate end-to-end time to solution. In prior work, we introduced SSZ, an error-bounded two-stage compressor that couples (i) a global, feature-oriented low-rank approximation computed via randomized sketching with (ii) a second stage that further compresses the resulting singular vectors using prediction-based compression under adaptive, singular-value–scaled tolerances, yielding a multiplicative gain in compression while retaining direct control of reconstruction error (NRMSE) [1]. This talk targets the next step needed by many multiscale PDE workflows: extending SSZ from structured grids to unstructured meshes typical of high-fidelity computational fluid dynamics in intricate domains (e.g., external aerodynamics of complicated bodies and multiscale structures of turbulent flows). We propose a mesh-aware formulation in which the second-stage predictor operates on mesh connectivity (graph neighborhoods and element adjacency) rather than Cartesian stencils, aligning the local compression stage with arbitrary and evolving geometries while preserving the global coherence captured by the low-rank stage. Building on modern prediction-based compressors and recent advances in error-controlled compression for unstructured data, we outline an SSZ pipeline suitable for multiscale ensembles and long time horizons, where repeated I/O and inter-site transfers are performance-critical [2,3,4]. The resulting framework aims to retain key flow structures across scales while materially reducing storage and data-motion costs in multiscale fluid dynamics.