International obligations to reduce carbon dioxide emissions and requirements to strengthen security of fuel supply, indicate a need to diversify towards the use of cleaner and more sustainable fuels. Hydrogen has been recommended as an encouraging gaseous fuel for future road transportation since with reasonable modifications it can be burned in conventional internal combustion engines without producing carbon-based tailpipe emissions. Direct injection of hydrogen into the combustion chamber can be more preferable than port fuel injection since it offers advantages of higher volumetric efficiency and can eliminate abnormal combustion phenomena such as backfiring. The current work applied a fully implicit computational methodology along with the Reynolds-Averaged Navier-Stokes (RANS) approach to study the mixture formation and combustion in a direct-injection spark-ignition engine with hydrogen fuelling. Hydrogen was issued into the combustion chamber by a six-hole side-mounted injector. The effects of two injection strategies, namely single and double-pulse injections per cycle, were examined whilst maintaining an equivalence ratio of 0.5 at part-load conditions of 0.5 bar intake pressure at 1,000 RPM. The combustion process was also computed using a ‘partially-premixed homogeneous reactor’ approach in conjunction with a detailed chemical kinetics combustion solver. The results were discussed in relation to previously published work on in-cylinder experiments of hydrogen engines.