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This work explores the use of surface-mesh flow solvers to model solid rocket internal ballistics with arbitrary grain geometry. Specifically, a surface-vorticity approach, originally intended for external flow applications, is adapted for internal flow analysis using boundary conditions that are suitable for solid rocket motors. In this study, an enhanced panel code is shown to be capable of resolving internal rocket flowfields with a striking level of fidelity and with such a degree of computational efficiency to make it valuable in the conceptual and preliminary design of rocket motors. In this process, the vortex paneling approach embodied within FlightStream® is refined using boundary conditions appropriate for solid rocket rotational flows. The simulation results are then compared to existing analytical solutions for cylindrical and planar chamber configurations exhibiting small taper angles and uniform headwall injection. For a more realistic validation case, the space shuttle's reusable solid rocket motor (RSRM) is examined. Guided by the analytical models, simple rotational and compressibility corrections are incorporated into the solver, and the results are subsequently compared to two other computational models and experimental measurements gathered from qualification motors. For the basic configurations, our results are shown to agree well with theoretical predictions. For the RSRM case, the corrected solution agrees well with the validation data in the first half of the motor; however, it becomes less robust in the aft region unless a recirculation zone boundary patch is applied; the latter approximates the added vorticity introduced by intersegmental gaps and the submerged nozzle effects.