On-the-fly reduced-order modeling of turbulent flames in Type Ia supernovae

A review is conducted of the state of progress in physical modeling and computational simulations of turbulent flames as pertaining to Type Ia supernovae. The continuum-level governing equations are simplified with various assumptions, to make a case for a more systematic inclusion of turbulence-reaction interactions for future investigations. We also report on recent progress made in using time-dependent subspaces for reduced-order modeling (TDB-ROM) of turbulent reacting flows with large number of isotopes. Unlike data-driven reduced-order modeling techniques, e.g. principal component analysis, TDB-ROM does not require any offline data generation and, as a result, TDB-ROM can adapt on-the-fly to changes in problem dynamics. First, a skeletal kinetics reduction technique is presented, in which the most important reactions and isotopes are detected in a detailed reaction network by on-the-fly reduced-order modeling of sensitivities. The generated skeletal models are then implemented in multi-dimensional simulations. The method is demonstrated for carbon-oxygen combustion under Type Ia conditions. Extensions of TDB-ROM in evolving isotopes transport equations are also discussed. This application of TDB-ROM decreases the computation and book-keeping costs by n_s/r, where n_s and r are the number of isotopes and reduction size, respectively.