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Modeling of macrosegregation benchmarks using a stabilized finite element algorithm based on a semi-implicit pressure correction scheme

Kangxin Chen (Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing, China)
Houfa Shen (Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 3 September 2019

Issue publication date: 16 January 2020

Abstract

Purpose

The purpose of this paper is to simulate two macrosegregation benchmarks with a newly developed stabilized finite element algorithm based on a semi-implicit pressure correction scheme.

Design/methodology/approach

A streamline-upwind/Petrov–Galerkin (SUPG) stabilized finite element algorithm is developed for the coupled conservation equations of mass, momentum, energy and species. A semi-implicit pressure correction method combined with SUPG stabilization technique is proposed to solve the convection flow during solidification. An analytically derived enthalpy method is adopted to solve the energy conservation equation. The nonlinearities of the energy and species equations are tackled by Newton–Raphson method. Two macrosegregation benchmarks considering the solidification of an Al-4.5 per cent Cu alloy and a Sn-10 per cent Pb alloy are simulated.

Findings

A very good agreement is achieved by comparison with the classical finite volume method and a novel meshless method for the Al-4.5 per cent Cu alloy solidification benchmark. Moreover, a unique reference numerical solution has been obtained. Besides, it is demonstrated that the stabilized finite element algorithm can capture the flow instability and channel segregation during solidification of the Sn-10 per cent Pb alloy.

Originality/value

A semi-implicit pressure correction method combined with SUPG stabilization technique is adopted to develop robust stabilized finite element algorithm for the macrosegregation model. A new enthalpy formulation for heat transfer problems with phase change is derived analytically.

Keywords

Citation

Chen, K. and Shen, H. (2020), "Modeling of macrosegregation benchmarks using a stabilized finite element algorithm based on a semi-implicit pressure correction scheme", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 2, pp. 918-933. https://doi.org/10.1108/HFF-10-2018-0544

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited