Semi-implicit method for thermodynamically linked equations in phase change problems (SIMTLE)

2Citations
Citations of this article
13Readers
Mendeley users who have this article in their library.

Abstract

Thermodynamic coupling of temperature and composition fields in phase-change problems has been a challenge for decades. A compromise has been always desired between numerical efficiency and detailed physical consideration, toward a general scheme. In the present work, a macro-micro numerical method is proposed to link the conservation equations of energy and species with the thermodynamics of the solidification problems. Firstly, the basic structure of the method, simplified with a local equilibrium assumption, is presented. The method is then extended to a multi-phase model, demonstrating a three-phase approach to the solidification of a eutectic binary alloy. Relaxing the limitations imposed by the equilibrium assumption, non-equilibrium and microscale considerations was also included subsequently by a suggested modification to the macroscopic mathematical model. Advantages gained through the general algorithm proposed are concerned with two features of the method; (a) consistency with the energy and species equations. (b) No need of a predefined solidification path; that allows for the usage of raw phase diagram curves and offers simplicity and generality for extension through complex problems (i.e. microscopic, multi-phase or non-equilibrium). A benchmark problem was employed to test the performance of the proposed method in two cases of local equilibrium and Scheil-like solidification. The obtained results were validated in comparison with available semi-analytical solution. © 2011 Elsevier Inc.

Cite

CITATION STYLE

APA

Jafari, A., Seyedein, S. H., & Aboutalebi, M. R. (2011). Semi-implicit method for thermodynamically linked equations in phase change problems (SIMTLE). Applied Mathematical Modelling, 35(10), 4774–4789. https://doi.org/10.1016/j.apm.2011.03.051

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free