The variation in seasonal precipitation intensity impacts the dynamic interaction between the karst aquifer and stream. However, the interaction mechanism between the karst aquifer and stream is currently still unclear, and characterizing the impact of dynamic saturation process of groundwater in karst media on the interaction process remains a challenge. To delve into the impacts of varying precipitation intensities, different water retention models, multi-stage conduit arrangements, and multiple precipitation events on the interaction process between the karst aquifer and stream, this study employs the multiphase Darcy-Brinkman-Stokes equation to analyze the interaction process between the karst aquifer and stream. Additionally, the Phase Indicator Function is used to capture the dynamic changes in saturation levels of various media, and the Brooks-Corey (BC) and van Genuchten-Mualem (VGM) equations are employed to characterize the soil-properties of porous media. The results show that as the intensity of precipitation increases, the interaction process between the karst aquifer and stream becomes more complex, involving the synergistic recharge of multi-media and dynamic interactions with the karst aquifer. Discharges in both upper (PM I) and lower (PM Ⅱ) porous media rise with precipitation intensity, but PM Ⅱ shows a more significant increase and earlier peak discharge. Secondly, during the middle to late stages of precipitation, the discharge predicted by the BC model exceeds that of the VGM model. The multi-stage conduit arrangement significantly affects stream and karst conduit hydrology during heavy precipitation but has less impact on other media. Finally, multiple precipitation events with different intensities could affect the ease of recharge from media in different strata of the karst aquifer. The Darcy-Brinkman-Stokes model can effectively simulate the interaction process between the karst aquifer and stream under the influence of precipitation. It can accurately depict the two-phase interactive flow between various media controlled by the dynamic saturation process, and reveal the dynamic interaction process between karst aquifers affected by the epikarst, sinkholes, and conduits under infiltration recharge and stream. Meanwhile, it can precisely explain the processes of infiltration, overflow, and recession.