Solving heat conduction problems with a moving heat source in arc welding processes via an overlapping nodes scheme based on the improved element-free Galerkin method

Abstract

A novel overlapping nodes scheme developed in the framework of an improved element-free Galerkin (IEFG) formulation is introduced in order to solve the transient heat conduction problem with a moving heat source involved in arc welding processes, in an accurate and remarkably simple manner. The proposed approach consists in solving the aforementioned problem over two overlapping arrangements of nodes, which transfer temperature and heat flux information each other through properly defined immersed boundaries. A fine arragement of nodes (patch nodes) moves with the heat source over a coarse background nodes distribution, and the solution is enriched via an appropriate coupling of the temperature approximations computed over both arrangements. The patch nodes are conceived to achieve an accurate computation of the temperature distribution and corresponding heat fluxes in the heat source vicinity, whose effects cannot be properly captured by the coarse background arrangement. A detailed explanation concerning the appropriate coupling between the temperature fields of both the background and patch nodes, is also provided in this communication. The outcomes of this study reveal that the proposed Overset-IEFG (Ov-IEFG) formulation allows the achievement of very accurate, smooth and stable solutions for both temperature and heat flux fields, without the need of resorting to post-processing or additional local reconstruction techniques.