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A coupled numerical approach is investigated for predicting combustion instability limit cycle characteristics when the combustor contains a long flame. The test case is the ORACLES combustor, with a turbulent premixed flame a metre long: it exhibits limit cycle oscillations at ∼ 50 Hz and normalised velocity amplitude ahead of the flame of ∼ 0.29. The approach obtains the flame response to acoustic excitation using Large Eddy Simulations (LES), and couples this with a low-order wave-based network representation for the acoustic waves within the combustor. The flame cannot be treated as acoustically compact; the spatial distribution of both its response and the subsequent effect on the acoustics must be accounted for. The long flame is uniformly segmented axially, each segment being much shorter than the flow wavelengths at play. A series of “local” flame describing functions, one for the heat release rate …