An overset improved element-free Galerkin-finite element method for the solution of transient heat conduction problems with concentrated moving heat sources

Abstract

A novel Overset Improved Element-Free Galerkin-Finite Element Method (Ov-IEFG-FEM) for solving transient heat conduction problems with concentrated moving heat sources is introduced in this communication. The method is a mesh-less/mesh-based chimera-type approach that utilises a coarse finite element mesh to discretise the problem geometry, while a separate set of overlapping nodes (patch nodes) moves with the heat source to capture the marked thermal gradients with higher accuracy using the Improved Element-Free Galerkin (IEFG) technique. Outside of the heat source area, where accuracy requirements are significantly lower, the thermal problem is solved using the Finite Element Method (FEM). The approach involves solving the problem over these two overlapping computational domains and transferring numerical information between the approximations performed on both. Such transfer of information occurs through immersed boundaries that are properly defined, enabling straightforward achievement of accurate results. The proposed Ov-IEFG-FEM is conceived to provide an enriched solution by appropriately coupling the temperature fields computed on the patch nodes and the coarse background mesh using IEFG and FEM, respectively. A comprehensive explanation concerning the appropriate coupling between the temperature fields of both the coarse background finite element mesh and the fine arrangement of moving patch nodes for the IEFG computations, is also provided in this communication. Numerical experiments demonstrate the method effectiveness in accurately and efficiently solving transient heat conduction problems with concentrated moving heat sources.