Phasewise numerical integration of finite element method applied to solidification processes

Abstract Phase change is a very complex physical phenomenon that governs a lot of industrial situations. Due to the inherent difficulties that arise in manufacturing activities they need a numerical treatment using models to predict the behavior of the different phases involved in the process. Historically, solidification problems were solved considering only the solution of an energy balance with isothermal phase change including conduction and or convection in the material. Nowadays computational fluid dynamics is becoming a well-suited numerical technique to investigate all kind of transport phenomena, especially when coupled fields are involved. This trend has addressed the research in solidification problems towards the solution of models combining incompressible Navier–Stokes equations coupled with heat and mass transfer including phase change. In this paper we present a phasewise discontinuous numerical integration method to solve thermal phase change problems in a fast and accurate way. Moreover, this methodology was extended to coupled fluid flow and energy balance equations with success and in a future work we will apply to binary alloy solidification with macrosegregation.

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