Solid Rocket Motors involve strongly coupled two-phase flow. The presence of a polydisperse spray of particles resulting from the combustion of aluminized propellant has been shown to have a strong impact on stability and can eventually yield thrust oscillations. The ability to conduct predictive simulations of such a harsh environment is highly desirable. Euler-Euler models relying on moment methods for the disperse phase constitute interesting approaches due to their efficiency at coupling both phases and their ability for high performance computing. A multi-fluid model coupled to a new numerical strategy for the disperse phase is introduced in order to cope with the natural high stiffness of the resulting systems of conservation laws. The predictive character of the method is strongly related to the possibility of using accurate methods while preserving stability and robustness in the presence of intrinsic singularities occurring in the disperse phase equations. The purpose of this contribution is to stress the impact of several numerics and modeling on the solution. Relevant test cases for solid propulsion involving hydrodynamic instabilities and acoustic coupling are presented. A strategy is proposed in order to produce reliable predictions.