In this paper, we present a numerical approach for predicting fluid flows in solid rocket motor (SRM) chambers. We use a novel high-order technique to track the burning grain surface. Spectral convergence toward the exact burning surface is achieved thanks to Fourier differentiation. In addition, we make use of a body-fitted mesh deforming with the burning surface and present a method to avoid manual remeshing. We describe several methods to deform the volume mesh and to keep good mesh element quality during the computation. We then couple the surface and volume approaches. The resulting coupled method is able to handle the formation of geometric singularities on the burning surface while keeping constant surface and volume mesh topology. This geometrical approach is integrated into a complex code for compressible, multi-species, turbulent flow simulations. Applications to the simulation of the internal flow in realistic solid rocket motors with complex grain geometry are then presented.
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