A combined solid and gas-phase numerical model has been developed and used to simulate the piloted ignition of a radiatively heated composite material in a boundary layer oxidizer flow. Condensed phase processes ( oxidative and thermal pyrolysis, phase change, and in-depth radiation absorption) are simulated with a pyrolysis model developed by the authors. The solid-phase model is coupled to a modified version of the CFD code Fire Dynamics Simulator (FDS), which provides a transient solution to the low Mach number, reactive, buoyant, Navier Stokes equations. The condensed phase and gaseous chemical kinetics are simplified with one-step Arrhenius reactions. Ignition occurs when a premixed flame propagates upstream from the igniter and forms a diffusion flame anchored at the surface of the solid fuel. Numerical simulations have been performed for a polypropylene/ fiber glass blended composite slab with a glass concentration of 30% by mass and thickness of 3.2 mm. The influence of the incident radiant heat flux, oxidizer flow velocity, and gravitational acceleration on piloted ignition of this composite material has been investigated. Emphasis is given to low-velocity microgravity flows expected in spacecraft. Ignition delay time predictions are compared with experimental data for several external heat flux levels and two flow velocities. The ignition time, pyrolysis rate at ignition, and surface temperature at ignition are considerably lower in a 0.09 m/s microgravity flow than in a 1.0 m/s normal gravity flow. This has important fire safety implications because it indicates that piloted ignition of solid combustibles will occur more easily under the conditions expected in spacecraft.