Numerical simulations are used to solve the coupled partial differential equations describing stimulated Brillouin scattering (SBS) built up from random thermal phonons as a function of time and the longitudinal spatial coordinate in an optical fiber. In the case of a passive fiber, a laser beam is incident with constant power, but its frequency is linearly ramped at 1.55 μm at a rate of up to 1016 Hz/s. High chirp rates lead to an increased Brillouin spectral bandwidth and decreased gain. The resulting SBS suppression is well described by an adiabatic model and agrees with experimental results. For an 18-m active fiber pumped at 1.06 μm and chirped at up to 2 × 1016 Hz/s, the suppression enables output laser powers in the kilowatt range while maintaining a narrow instantaneous linewidth.