Gas turbines for power generation use lean premixed flames to adhere to the strict pollutant emissions regulations. Unfortunately, this often leads to thermoacoustic instabilities. These instabilities can lead to failure of system components, flame blow-off or flashback and a reduction in efficiency. Especially the high frequency transverse thermoacoustic instabilities can lead to big problems in the successful operation of gas turbines. These instabilities can be reduced by adding damping devices or mitigating the excitation mechanisms. In this work, Large Eddy Simulation (LES) is used to identify the thermoacoustic instability which tends to occur in a specific heavy duty gas turbine combustor design. In order to successfully counteract this instability, identification of the acoustic mode affecting the burner is required. Results from the LES are compared with experiments to test the predictability of LES and research mitigation techniques. The oscillation amplitudes do not match due to numerical damping, but the frequency of the oscillation in LES is within 1% of the experimental value. Furthermore, a coherence between the heat release and pressure oscillations of 80% is achieved and the phase of the oscillations are within 90° of each other. This confirms that the Rayleigh criteria is satisfied and the instability in the simulation is indeed a self-excited thermoacoustic instability. After identifying the mode, Fast Fourier Transform (FFT) of the pressure data at the combustor walls is used to visualize and locate the mode. Its location suggests that fuel supply oscillations could be a possible driving mechanism. However, the frequency of the oscillations in the fuel supply did not match that of the thermoacoustic instability so this hypothesis was rejected. After identifying the mode, the effect of different simulation and operation parameters is researched. First a model coefficient which influences the flame length is changed. Shortening the flame results in a higher amplitude instability, due to the location of maximum heat release moving closer to the location of the source of the instability. Next, the fuel distribution is changed in order to break flame symmetry and reduce the instability amplitude. This is done successfully, as the amplitude of the instability at the peak frequency is reduced to the same level as the surrounding noise frequencies. Finally, the effect of adding Helmholtz resonators specifically designed for the instability of interest is researched. A transfer function is defined to measure the response of the resonators to a pressure fluctuation in front of them. The result is compared to an analytical solution to determine the effectiveness of the resonators. Like the fuel biasing, also the resonators performed well and resulted in a decrease of the instability amplitude.