Overlapping improved element-free Galerkin and finite element methods for the solution of non-linear transient heat conduction problems with concentrated moving heat sources

A novel overlapping approach, termed the Overset IEFG-FE method (Ov-IEFG-FEM), is proposed for solving transient heat conduction problems with concentrated moving heat sources. This mesh-less/mesh-based chimera-type method combines improved element-free Galerkin (IEFG) and finite element (FE) methods. The Ov-IEFG-FEM uses a coarse FE mesh to discretise the problem geometry, while a set of overlapping patch nodes moves with the heat source, enhancing accuracy via the IEFG technique to capture marked thermal gradients. In regions outside the heat source area where accuracy requirements are lower, the thermal problem is solved using the FE method (FEM). The method involves solving the problem over these two overlapping domains and transferring numerical information between the approximations performed on both. The Ov-IEFG-FEM aims to provide an enriched solution by coupling temperature fields computed on the patch nodes and the coarse background mesh using IEFG and FE methods, respectively. Numerical experiments demonstrate the method potential in accurately and efficiently solving transient heat conduction problems with concentrated moving heat sources, including marked non-linear aspects related to temperature-dependent properties and phase change phenomena.