The objective of the PhD study is to optimize the injector design for an RDC fed with gaseous hydrogen and air. An optimized injector must provide efficient mixing, while limiting total pressure losses. The available time to mix the reactants is on the order of 100 µs, depending on the number of waves and their propagation speed. Several injection principles and geometries (shape, size and orientation of the orifices) will be compared according to the mixing efficiency and total pressure recovery criteria. These criteria will be evaluated from simulation results using LES for the turbulent mixing in an RDC. The best configuration will be studied in more detail and further improved. Injector operation will be characterized in a cold-flow continuous regime, then in a reactive reinjection regime in order to extend understanding of the injection and mixing processes occurring in a RDC. The optimized injector design will be tested on the experimental RDC of TUB in the scope of DC01. In parallel, first simulations of the operation of the TUB RDC will be set up to select the appropriate numerical methods and physical models. Post-processing tools will be developed to analyse the mixture formation in the RDC. The experimental study by DC01 will make it possible to select an operating point of interest to be simulated by DC04. The numerical results of DC04 and the experimental results of DC01 can thus be compared. If necessary, the numerical approach will be tuned to achieve agreement with the detonation propagation speed and pressure signals in the experimental RDC. The final simulation results will provide detailed information about the mixture formation in the RDC and its interaction with propagating detonation waves. Additional mixing simulations of the optimized injector in the radial RDC configuration of DC14 will be performed.