Implementation of a standard stream-upwind stabilization scheme in the element-free Galerkin based solution of advection-dominated heat transfer problems during solidification in direct chill casting processes

Abstract

The present work has been conducted in order to propose an alternative solution for the heat transfer problem involved in direct-chill casting (DCC) processes, employing the element-free Galerkin (EFG) method. The internal energy balance has been solved on the basis of this global weak formulation under an Eulerian description. The EFG formulation has been adapted to a three-dimensional steady thermal problem on an aluminum alloy slab. Additionally, the advection dominated problem involved in the casting direction during the liquid-solid phase change has been stabilized by extending adequately the implementation of the stream upwind Petrov–Galerkin (SUPG) scheme to the EFG formulation. A detailed explanation concerning the suitable numerical procedure to achieve such an extension, has also been provided. The feasibility and reliability of this novel approach has been depicted by comparison with both finite element method (FEM) and finite volume method (FVM) based solutions. The results have demonstrated that a proper extension of the SUPG scheme to the EFG method allows the achievement of stable numerical solutions, when predicting the three-dimensional temperature distribution during the phase-change heat transfer phenomena involved in slab DCC processes.