The subject of this thesis is the development of a method for the numerical simulation of gasoline self-ignition. In addition to the calculation of non-reacting flows with moving and stationary computational grids, a piloted methane-air jet flame is simulated. In addition, the work gives an outlook on the treatment of a near-production single-cylinder 4-stroke gasoline engine with direct injection in compression-ignition mode. The developed numerical method is based on a time-resolved, three-dimensional description of the gas and the disperse phase...