Element-Free Galerkin Meshless Method on Solidification Behavior Inside Continuous Casting Mold

Abstract

Compared with mesh-based numerical approaches, the meshless methods avoid complex topology and transmission of nodal information, which shows remarkable advantages in solving the problems of phase-transition interface tracking, curved boundary and crack propagation. In this paper, the discrete governing equations of heat transfer/solidification for the round billet are deduced and constructed based on Element-free Galerkin method. Using the measured non-uniform heat flux to impose the Neumann boundary conditions, a 2D cross-section computational model is developed to simulate and investigate the non-uniform solidification behavior of round billet. In the computational model, the essential issues such as time discretization scheme, time step length, nodal arrangement and their effects on the simulation accuracy as well as stability are specified. To verify the influence and flexibility of node layout in the meshless method model, the present work explores a concentric circular nodal arrangement scheme and determines a reasonable range of nodal spacing. The result has revealed that the meshless method could be employed successfully in exploring the non-uniform solidification behavior of continuous casting billet, which provides a foundation for further research on thermo-mechanical and cracks propagation analysis.