Simulation of the transport of ions and neutral particles is important for studies of the flow field and working characteristics of jet flow plasma devices. The spatiotemporal evolution of plasma plumes in the small space within such devices is complex. To realize numerical simulations of particle transport in this situation, a variety of complex effects need to be considered, such as collisions between particles, chemical reactions, gas–surface interaction, and the electric field. In this study, five types of particles (H2, H, metal atoms, $\text{H}_{2}^{+}$ , and H+) are injected into a double-cylinder calculational domain. The direct simulation Monte Carlo (DSMC) method is used to simulate the spatiotemporal evolution of particles in the Maxwell and Cercignani–Lampis–Lord model with different accommodation coefficients. The particle accumulation phenomenon is explained, and the influence of the accommodation coefficient is elucidated. Wall chemical reactions are then introduced to make the gas–surface coupling more realistic. These reactions are found to have a great influence on the particle number density of H+, H2, and H, while the flow field structure has little influence, which is due to the small differences in the particle velocity distributions of each component. Finally, a DSMC/particle-in-cell method is used to simulate a simple axisymmetric example, and the influence of gas–surface interaction, wall chemical reactions, and the electric field on the spatiotemporal evolution of H2, H+, and H in the flow field is demonstrated.