Data-driven eigensolution analysis based on a spatio-temporal Koopman decomposition, with applications to high-order methods

Abstract

We propose a data-driven method to perform eigensolution analyses and quantify numerical errors in a non-intrusive manner. In classic eigensolution analysis methods, explicit matrices need to be constructed, whilst in our approach only solution snapshots from numerical simulations are required to quantify the numerical errors (dispersion and diffusion) in time and/or space. This new approach is based on a recent data-driven method: the Spatio-Temporal Koopman Decomposition (STKD), that approximates spatio-temporal data as a linear combination of standing or travelling waves growing or decaying exponentially in time and/or space. We validate our approach with classic matrix-based approaches, where accurate predictions of the dispersion-dissipation behaviour for both temporal and spatial eigensolution analyses are reported.