During the combustion of hydrogen, no carbon dioxide is released, but nitrogen oxides are produced due to the high temperatures when using air as oxidizer. Operation with pure oxygen offers the advantage that nitrogen oxide emissions can be avoided while simultaneously reducing fuel consumption. An innovative, two-stage burner geometry, designed for hydrogen/air combustion in the megawatt range, is to be investigated for operation in hydrogen/oxygen combustion mode. The burner is designed in such a way that a lifted, aerodynamically stabilized flame is generated away from the burner outlet. This minimizes the thermal load on the burner walls, which is particularly important in oxygen operation mode. The aim of the study is to validate the burner geometry for oxygen operation using reactive, numerical simulation. The focus is put on the thermal load on the burner walls, whereby the maximum permissible wall temperature was set to 750 °C. The flame is characterized by a steady-state flamelet approach. The burner walls are designed as solids and the heat flow is bidirectional. Air operation serves as a reference for the other operating conditions with increasing oxygen concentration (30 vol.-%, 50 vol.-%, 100 vol.-%), whereby a method used in industry for flame temperature control in oxygen operation mode via flue gas recirculation was also investigated. The results show that the thermal load on the burner walls in air operation is within the tolerance range. Short-term operation for experiments with 30 vol.-% oxygen-enriched air as well as the operation case with flue gas recirculation are possible, while the maximum permissible wall temperature of the burner is clearly exceeded from an oxygen content of 50 vol.-% in the air. Contrary to expectations, no lifted, aerodynamically stabilized flame is generated, but the flame anchors itself to the fuel injectors. No experimental data is available at the time of this study. However, a comparison of the simulated and experimental data is planned, with the focus on investigating the actual flame shape and position as well as the turbulent mixing process.