Understanding plume-surface interactions is essential to the design of lander modules and potential bases on bodies such as the Moon, as it is important to predict erosion patterns on the surface and the transport of the displaced regolith material. Experimentally, it is difficult to replicate the extra-terrestrial conditions (e.g. the effects of reduced gravity). Existing numerical tools have limited accessibility and different levels of sophistication in the modelling of regolith entrainment and subsequent transport. In this work, a fully transient open source code for solving rarefied multiphase flows, rarefiedMultiphaseFoam, is updated with models to account for solid-solid interactions and applied to rocket exhaust plume-lunar regolith interactions. Two different models to account for the solid-solid collisions are considered; at relatively low volume fractions, a stochastic collision model, and at higher volume fractions the higher fidelity multiphase particle-in-cell (MPPIC) method. Both methods are applied to a scaled down version of the Apollo era lunar module descent engine and comparisons are drawn between the transient simulation results. It is found that the transient effects are important for the gas phase, with the shock structure and stand-off height changing as the regolith is eroded by the plume. Both models predict cratering at early times and similar dispersion characteristics as the viscous erosion becomes dominant. In general, the erosion processes are slower with the multiphase particle-in-cell method because it accounts for more physical effects, such as enduring contacts and a maximum packing limit. It is found that even if the initial volume fraction is low, the stochastic collision method can become unreliable as the plume impinges on the surface and compresses the regolith particles, invalidating the method’s assumption of only binary collisions. Additionally, it is shown that the breakdown of the locally free-molecular flow assumption that is used to calculate the drag and heat transfer on the solid particles has a strong influence on the temperatures that the solid particles obtain.