A low cost singular value decomposition based data assimilation technique for analysis of heterogeneous combustion data

This article applies low-cost singular value decomposition (lcSVD) for the first time, to the authors knowledge, on combustion reactive flow databases. The lcSVD algorithm is a novel approach to SVD, suitable for calculating high-resolution 2D or 3D proper orthogonal decomposition (POD) modes and temporal coefficients using data from sensors. Consequently, the computational cost associated with this technique is much lower compared to standard SVD. Additionally, for the analysis of full n-dimensional datasets, the method reduces data dimensionality by selecting a strategically reduced number of points from the original dataset through optimal sensor placement or uniform sampling before performing SVD. Moreover, the properties of data assimilation of heterogeneous databases of this method are illustrated using two distinct reactive flow test cases: a numerical database modeling an axisymmetric, time-varying laminar coflow flame with a fuel mixture of 65% methane and 35% nitrogen, using air as the oxidizer, and experimental data generated from a turbulent bluff-body-stabilized hydrogen flame. The computational speed-up and memory gains associated with the lcSVD algorithm compared to SVD can reach values larger than 10, with compression factors greater than 2000. Applying lcSVD for data assimilation to reconstruct the flow dynamics combining data from sensors with simulation measurements, we found errors smaller than 1% in the most relevant species modelling the flow.