  The combustion instability is investigated computationally for a
multi-injector rocket engine using the flamelet progress variable (FPV) model.
A C++ code is developed based on OpenFOAM 4.0 to apply the combustion model.
Flamelet tables are generated for methane/oxygen combustion at the background
pressure of $200$ bar using a 12-species chemical mechanism. A power law is
determined for rescaling the reaction rate for the progress variable to address
the pressure effect. The combustion is also simulated by the one-step-kinetics
(OSK) method for comparison with the FPV approach. A study of combustion
instability shows that a longitudinal mode of $1500$ Hz and a tangential
standing wave of $2500$ Hz are dominant for both approaches. While the
amplitude of the longitudinal mode remains almost the same for both approaches,
the tangential standing wave achieves a larger amplitude in the FPV simulation.
A preliminary study of the resonance in the injectors, which is driven by the
longitudinal-mode oscillation in the combustion chamber, is also presented.
