High-Fidelity 4D Flow Assimilation via Hard-Constrained Pseudo-Spectral Meshless Track Assimilation

Meshless Track Assimilation (MTA) provides exceptional accuracy for the 4D Data Assimilation (DA) of Particle Tracking Velocimetry (PTV) data, but its widespread adoption has been bottlenecked by prohibitive computational times, massive memory constraints, and tedious hyperparameter tuning. This work introduces a transformative pseudospectral paradigm for MTA by kernelizing compact-support Radial Basis Functions (RBFs), shifting the computational core from expensive sparse matrix products to highly efficient FFT-based convolutions. Furthermore, by embedding the divergence-free condition as a hard spectral constraint and analytically eliminating pressure via variable projection. The overhauled formulation achieves a 20x computational speedup and slashes the DA operator memory footprint from 170 MB to just 2.5 MB while preserving or improving reconstruction accuracy. Crucially, this framework democratizes the method, making fully coupled, billion-variable 4D flow reconstructions feasible in-core on consumer-grade PC hardware with virtually no parameter tuning.