The paper describes one of the steps of the numerical modeling of a cycle for a direct injection engine. The fuel injection is considered in the form of a gaseous isothermal non reacting jet which mixes with surrounding air in free or in confined situations. The model uses the equations of conservation of mass, momentum and energy. The domain is mapped with non uniform rectangular cells in cartesian, or axisymmetrical, or polar coordinates. The conservation equations are discretized in a finite difference way and are solved by a semi-implicit I.C.E. method. This theoretical model is applied to the study of the mixing of methane with air for an impulsively started round free jet and for a round jet impinging on a flat plate. In polar coordinates, the injection of methane, through four periodic slots, in confined swirling or non-swirling air is simulated, approaching the diesel engine configuration.