Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

This work presents a hybrid formulation combining the Method of Fundamental Solutions (MFS) and the Method of Particular Solutions (MPS) coupled with an implicit Finite Difference Method (FDM) to simulate the transient heat conduction in a two-layer domain composed of a steel tool and an epoxy resin. The proposed approach incorporates a non-homogeneous source term in the governing equation, allowing the analysis of the curing heat release within the resin layer while maintaining a meshless boundary-based structure. Sequential numerical tests were performed to empirically assess the influence of key hyper-parameters number and position of source points, distance parameters, and the Tikhonov regularization factor on the stability and accuracy of the method. The MFS-MPS/FDM model showed excellent agreement with the finite element results reported by Dei Sommi et al., achieving low RMSE and MAE values relative to the thermal scale of the process. These results confirm the robustness and predictive capability of the MFS in capturing transient thermal evolution even in the presence of a source term, although its performance remains sensitive to the proper calibration of numerical hyper-parameters.