High-Fidelity h-Adaptive Finite Element Simulation of Transient Thermal Fields in Laser-Based Additive Manufacturing
O.A, Olaiju
Department of Mathematics and Statistics, Federal Polytechnic Ilaro, Nigeria.
E. O. Fatunmbi
*
Department of Mathematics and Statistics, Federal Polytechnic Ilaro, Nigeria.
O. A. Agbolade
Department of Mathematics and Statistics, Federal Polytechnic Ilaro, Nigeria.
J. K. Odeyemi
Department of Mathematics and Statistics, Federal Polytechnic Ilaro, Nigeria.
O. C. Akeremale
Department of Mathematics, Federal University of Lafia, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a high-resolution h-adaptive Finite Element Method (FEM) framework for simulating transient heat conduction in laser-based additive manufacturing (AM). The approach solves the 2D heat equation with a moving Gaussian heat source, using residual-based a posteriori error estimation and Dörfler marking to drive local mesh refinement. Linear triangular elements and implicit Euler time integration are combined with nearest-neighbour solution prolongation on adaptively regenerated meshes. Validation against manufactured solutions demonstrates exponential convergence in both L² and energy norms. Applied to a moving heat source problem, the method accurately captures melt pool dynamics while minimizing computational overhead. Numerical results highlight up to 90% reduction in computational cost compared to uniform refinement. This makes the method well-suited for predictive thermal modelling and real-time simulation in industrial AM applications.
Keywords: Adaptive finite element method, transient heat conduction, moving gaussianheat source, h-adaptive mesh refinement, numerical simulation, nomenclature