Numerically modelling the multi-physics phenomenon of combustion is challenging as it involves fluid flow, chemical reaction, phase change, energy release, etc. Combining numerical models for all these phenomena into a single solver ensuring scalability and performance is a daunting task. Based on the hierarchical meshing technique building cube method (BCM) we present a numerical framework for modelling internal combustion engines. The framework efficiently combines a fully compressible flow solver, chemical reaction and combustion model, a particle-in-cell based liquid spray model, and an immersed boundary method for geometry treatment. The flow, temperature fields and the transport of reacting species an all speed Roe scheme is adopted discretization of the advective flux. The solver is coupled with the equilibrium chemical reaction library CANTERA to model combustion. The parcel model-based particle-source-in-cell (PSI-cell) method is adopted for modelling liquid fuel spray and its evaporation. Validation of the numerical framework is carried out by using experimental data of a model internal combustion engine known as the Rapid Compression Machine (RCM). Evaluation of the framework with strong scaling analysis shows good scalability.