The present paper is devoted to three-dimensional numerical simulations of reactive two-phase flows in interior and transitional ballistics. The model presented takes a variety of phenomena into account such as mass transfer by the combustion of complex grain geometries, drag force experienced by the propellant bed in the gas flow, and convective and radiative heat transfer between the solid and the gaseous phase to simulate the process of ignition. A multi-dimensional finite volume scheme based on a nonconservative two-velocity one-pressure model is deployed to compute the pressure distribution in a 40mm weapon system, the velocity of the projectile, and the flow field of the muzzle flash. Comparisons between the obtained results and experimental findings, as well as the predictions of state-of-the-art lumped-parameter codes, show good agreement and serve as a validation. Finally, interior ballistics simulations involving novel grain geometries are discussed which exhibit more effective combustion properties as compared to conventional grains and thus lead to enhanced performances.