A fully conservative explicit scheme for a solid-particle-laden gas flow in a convergent-divergent nozzle is studied numerically as a direct time-dependent problem for a one-dimensional flow. The initial conditions at t = 0 are taken from the similarity solution. The boundary conditions at the nozzle inlet are determined by taking an arbitrary large cross-section at the first grid point before the nozzle inlet and are held constant with time. The exit boundary conditions are obtained at the grid point next to the exit plane from the values extrapolated at the exit plane. The particle burning rate is assumed to be a function of pressure. A time-dependent predictor-corrector formulation with a fourth-order damping term is used. Convergence of the result is assumed when the throat Mach number change is <0.0001, generally in ≤ 400 time steps. © 1989.