Low-Rank Approximation with Time-Dependent Bases for Uncertainty Quantification Turbulent Reactive Flows

In turbulent reactive flows, developing accurate and tractable predictive models encounters a significant barrier due to the need to solve a large number of chemical species, resulting in computational expense. Specifically, when considering uncertain kinetic coefficients, the problem becomes impracticable as it requires solving the spatio-temporal partial differential equations for all species numerous times.

This study addresses the challenge of uncertainty quantification in such reactive flows, focusing on perturbing 34 kinetic coefficients. The dimensionality of the problem is substantial, calculated as the product of the number of grid points (19076), species (11), and random samples (10000), resulting in a total of roughly 2*10⁹. Traditional uncertainty quantification methods struggle to handle such high-dimensional problems efficiently.

To overcome this challenge, we propose a novel approach that combines using low-rank approximation with time-dependent bases to significantly reduce the computational cost of solving this problem. By integrating these techniques, we aim to address the computational infeasibility associated with traditional Monte Carlo simulations.