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The combustion of gaseous fuels like methane in internal combustion engines is an interesting alternative to the conventional gasoline and diesel fuels. Reasons are the availability of the resource and the significant advantage in terms of CO2 emissions due to the beneficial C/H ratio. One difficulty of gaseous fuels is the preparation of the gas/air mixtures for all operation points, since the volumetric energy density of the fuel is lower compared to conventional liquid fuels. Low-pressure port-injected systems suffer from substantially reduced volumetric efficiencies. Direct injection systems avoid such losses; in order to deliver enough fuel into the cylinder, high pressures are however needed for the gas injection which forces the fuel to enter the cylinder at supersonic speed followed by a Mach disk. The detailed modeling of these physical effects is very challenging, since the fluid velocities and pressure and velocity gradients at the Mach disc are very high.