A reduced-order code based on a Garlerkin modal expansion of the pressure oscillations is presented to predict high frequency combustion instabilities in liquid rocket engines. Models to account for acoustic damping are proposed, such as nozzle, thermal or viscous losses. A combustion source term modeling the fuel inflow modulation of a coaxial injection unit through a flame transfer function is derived. A first application is made on the NPCC test bench, retrieving LES data with a nonlinear representation of the damping. Then the BKD combustor of DLR is simulated, and first comparisons with LES results are proposed.