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A new Computational Fluid Dynamics (CFD) code has been developed in order to overcome the deficiencies of traditional grid generation and mesh motion methods. The new code uses a modified cut-cell Cartesian technique that eliminates the need for the computational grid to coincide with the geometry of interest. The code also includes state-of-the-art numerical techniques and sub-models for simulating the complex physical and chemical processes that occur in engines. Features such as shared and distributed memory parallelization, a multigrid pressure solver and user-specified grid embedding allow for efficient simulations while maintaining the grid resolution necessary for accurate engine modeling. In addition, a new Adaptive Grid Embedding (AGE) technique has been developed and implemented. Sub-models for turbulence, spray injection, spray breakup, liquid drop dynamics, ignition, combustion and emissions are also included in the code.