This paper presents the numerical simulation of the gas-solid combustion physics in a gun tube with a mobile projectile by means of a flux-corrected transport nonlinear filtering scheme. The analysis is based on a one-dimensional formulation of the two-phase flowfield with the space-sharing interspersed continuum assumption. Apart from the Nobel-Abel equation of slate account the interphase drag and intergranular stress between the solid-gas phase are taken into account. The computer code has been used effectively to study the pressure-wave propagation and flame dynamics in a gun barrel containing granular solid propellants.