<p>The heterogeneity of karst aquifers, characterized by the coexistence of matrix, fractures, and conduits, poses significant challenges for simulating precipitation–discharge processes. Equivalent continuous models lose simulation accuracy because they neglect structural features, while fully discrete models have high meshing complexity and computational cost. To combine the high efficiency of equivalent continuous models with the high accuracy of discrete models in portraying system structures, a triple media (matrix–fractures–conduits) coupling model is developed in this study. An embedded discrete fracture model (EDFM) is used to characterize the fracture distribution in the matrix and a nodal conduits model is used to calculate water entering conduits from matrix and fractures. The performance of the numerical framework is tested using a synthetic model and an actual test site. In the synthetic case, spring discharge curves closely match those from a COMSOL-based discrete model (RMSE &lt; 0.01) while achieving a 53% improvement in computational efficiency. Application to the field site further validates the model and highlights how distinct media interactions shape discharge behavior. To investigate the influence of matrix, fractures, and conduits on spring discharge curves, scenario analyses are conducted by varying fracture network density, conduit position, and matrix permeability. Results reveal that vertical infiltration in the unsaturated zone is primarily driven by preferential flow through fractures. Conduits govern rapid spring discharge responses, whereas the matrix contributes delayed and sustained discharge. These differentiated flow dynamics collectively explain the observed multi-peak characteristics of spring discharge curves.</p>