A fractional-step, mixed explicit/semi-implicit method for calculating air flow inside engines is proposed and discussed. By splitting geometrically in terms of directions, the fractional-step method reduces the multidimensional governing equations to 1D systems of equations with the same form that can be solved by a unique and suitable 1D method. It combines two different numerical methods through a parameter 0≤ θ≤ 1: for θ= 0 it reverts to a semi-implicit method; while it is an explicit method for θ= 0. Accuracy and stability are proved for all values of θ. Numerical experiments have been worked out and comparisons with the KIVA II code have been made.