Introducing non-locality into solidification models

Vaughan R. Voller

doi:10.1007/s12666-012-0188-8

Introducing non-locality into solidification models

Vaughan R. Voller

Civil, Environmental, and Geo- Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A non-local flux, constructed as a weighted sum of local gradients, is introduced into a standard solidification model. A particular choice of weights leads to a flux expressed as a Caputo fractional derivative. Numerical solution, indicates that-in modeling solidification at microstructure scales of ∼5 mm-the presence of non-locality influences the distribution of temperature and liquid fraction and also increase the expected exponent in the characteristic solidification time scale.

Original language	English (US)
Pages (from-to)	515-519
Number of pages	5
Journal	Transactions of the Indian Institute of Metals
Volume	65
Issue number	6
DOIs	https://doi.org/10.1007/s12666-012-0188-8
State	Published - Dec 2012

Keywords

Enthalpy solution
Fractional derivative
Non-locality
Solidification model

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AB - A non-local flux, constructed as a weighted sum of local gradients, is introduced into a standard solidification model. A particular choice of weights leads to a flux expressed as a Caputo fractional derivative. Numerical solution, indicates that-in modeling solidification at microstructure scales of ∼5 mm-the presence of non-locality influences the distribution of temperature and liquid fraction and also increase the expected exponent in the characteristic solidification time scale.

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KW - Fractional derivative

KW - Non-locality

KW - Solidification model

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Introducing non-locality into solidification models

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Keywords

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