Exploration of POD-Galerkin Techniques for Developing Reduced Order Models of the Euler Equations.

摘要

Investigations of relevant issues involved in developing a reduced order model (ROM) are performed for describing combustion response to specific excitations using Euler equations as a continued work from a previous studies using a reaction-advection scalar equation. The ROM is obtained by employing Galerkin's method to reduce the high-order PDEs to a lower-order ODE system by means of POD eigen-bases. For purposes of this study, a linearized version of the Euler equations is employed. The knowledge obtained from previous scalar equation studies is applied to ROM development of Euler equations. Numerical stability issues are encountered in Euler equation studies, the cause of which is narrowed down to normalization methods for vector variables. The effects of normalization methods are then further assessed in terms of the ROM characteristics and its predictive capability.