Low-Rank Approximation of Filter Density Function Using Time-Dependent Bases

A new low-rank approximation based on time-dependent bases is developed for reduced-order modeling (ROM) of the scalar filtered density function (FDF). The ROM is based on a unified residual-minimization technique and is shown to be superior to conventional PCA-based schemes. This is due to the inherent flexibility of the method in allowing the temporal evolution of its subspace. The resulting model is employed in LES-FDF of a non-premixed CO/H_2 flame in a temporally evolving jet. For combustion chemistry, the syngas model involving 11 species is used. The results are appraised via a posteriori comparisons against data generated via full-rank LES-FDF and DNS of the same flame. The model yields excellent predictions of various statistics of the filtered thermo-chemistry variables.