On-the-fly reduced order modeling of passive and reactive species via time-dependent manifolds

One of the principal barriers in developing accurate and tractable predictive models turbulent flows with a large number species is to track every by solving separate transport equation, which can be computationally impracticable. In this paper, we present an on-the-fly reduced order modeling reactive as well passive equations reduce computational cost. The presented approach seeks low-rank decomposition three time-dependent components: (i) set orthonormal spatial modes, (ii) factorization instantaneous correlation matrix, (iii) represents low-dimensional manifold. Our bypasses need solve full-dimensional generate high-fidelity data — it commonly performed data-driven dimension reduction techniques such principle component analysis. Instead, components are directly extracted from equation. evolution for obtained optimality conditions variational principle. time-dependence enables adaptation transient changes species. Several demonstration cases presented.