This work reports preliminary results on the application of projection-based reduced-order models (ROMs) to the study of combustion dynamics in liquid-fueled rocket engines. Specifically, quasi-one-dimensional and axisymmetric (two-dimensional) models of a single element rocket combustor are explored. In the one-dimensional case, a POD-Galerkin-based ROM is shown to accurately reproduce the evolution of pressure perturbations over a wide region in parameter space. Next, the viability of sampling/interpolation techniques in accelerating ROM solutions is explored. Three techniques - the discrete empirical interpolation method (DEIM), a QR decomposition-based DEIM (QDEIM) and an adaptive technique (ADEIM) are used to reconstruct the solution in the entire domain based on sparse samples. All three techniques are shown to yield a low reconstruction error based on a very small fraction of sampling points (< 1% for the axisymmetric case). The ADEIM, by virtue of dynamically adapting the basis functions and sampling points, is seen to reduce the reconstruction error considerably in comparison to the DEIM/QDEIM, suggesting its viability in predictive ROMs of realistic rocket combustors.
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