A multi-fidelity framework oriented towards efficient modeling of combustion instability is established by integrating a reduced-order model (ROM) for combustion response into the linearized Euler equations. The ROM is developed from CFD simulations of periodic forcing of a combusting flow on a reduced domain using Galerkin's method to reduce the high-order PDEs to a low-order ODE system via POD eigen-bases generated from the reduced-domain dataset Evaluations of the framework are performed based on parametric studies of a simplified test problem for a model rocket combustor showing distinguishable instability behavior. Two-way information transfer between the two solutions is accomplished by interface matching at the reduced-domain boundaries. Accurate predictions require the use of multiple ROMs to account for both upstream- and downstream-traveling perturbations. In addition characteristic boundary conditions must be used at both reduced-domain boundaries to minimize wave reflections and preclude generic unstable responses in the multi-fidelity model prediction. Comparisons with full CFD solutions show the multi-fidelity model is capable of capturing overall instability trends.
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