An h-Adaptive Finite Element Method for Transient Thermal Analysis in Laser-Based Additive Manufacturing

This paper presents a transient 2D finite element solver with h-adaptive mesh refinement for simulating heat transfer in laser-based additive manufacturing (AM). The governing equation is the time-dependent heat conduction equation with a moving Gaussian heat source, modeling the laser beam interaction with powder bed material. A posteriori error estimation based on nodal temperature variation drives local mesh refinement around regions of steep thermal gradients. Linear triangularP ₁ elements are used, and mesh regeneration via Delaunay triangulation ensures conformity after each refinement step. The temporal discretization is performed using the implicit Euler method, and the solution is prolonged to the new mesh using nearest-neighbor interpolation. Numerical results demonstrate accurate resolution of the moving melt pool and exponential decay in element-wise error indicators under adaptive refinement. The method is well-suited for simulating laser scanning processes in AM with high spatial and temporal accuracy while maintaining computational efficiency.