Balancing Transformation for Lightly-damped Dynamics of a Forced Flame using the Eigensystem Realization Algorithm

Increasing applications of reduced-order models (ROMs) in transport problems and the long-standing demand for predictive ROMs encourage further research to reinforce model reduction techniques that leverage theoretical error bounds. The most promising of such methods is balanced truncation (BT) that employs Markov parameters to transform the system to equally controllable and observable coordinates. Stability is preserved under order reduction and the rich dynamical content of the impulse response enables prediction far from the training regime. In this work we utilize BT for model reduction of one-dimensional reacting flow with pressure forcing. Due to the stiffness introduced by the chemical source term we resort to the eigensystem realization algorithm to compute the balancing transformation. We study the sensitivity of the balanced ROMs with respect to sampling properties and show that the system undergoes lightly-damped oscillations following the initial transients, which poses additional computational bottlenecks. We demonstrate the robust performance of BT in comparison to the standard Galerkin and the least-squares Petrov-Galerkin projections in a purely predictive setting.