Cross-Correlation Snapshot Registration for Transport-Dominated Model Reduction
A model-order-reduction technique for transport-dominated PDEs (travelling waves, convective vortices) whose solution manifolds have slowly decaying Kolmogorov n-width and so resist linear reduction. Each snapshot is registered to a reference by the spatial shift that maximizes their cross-correlation; this transformation aligns the moving features, accelerating n-width decay so that a linear POD basis becomes effective. A complete offline-online framework then builds a non-intrusive (data-driven) reduced-order model via proper orthogonal decomposition with regression (POD-R) on the registered snapshots.
Model Reduction for Transport-Dominated Problems via Cross-Correlation Based Snapshot Registration
Gowrachari, Stabile and Rozza address the failure of linear model-order-reduction methods (proper orthogonal decomposition, reduced basis) on transport-dominated problems, where the Kolmogorov n-widt…