A fully implicit, fully adaptive time and space discretisation method for phase-field simulation of binary alloy solidification

Rosam, J., Jimack, P.K. and Mullis, A. (2007) A fully implicit, fully adaptive time and space discretisation method for phase-field simulation of binary alloy solidification. Journal of Computational Physics, 225 (2). pp. 1271-1287. ISSN 0021-9991

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Abstract

A fully-implicit numerical method based upon adaptively refined meshes for the simulation of binary alloy solidification in 2D is presented. In addition we combine a second-order fully-implicit time discretisation scheme with variable steps size control to obtain an adaptive time and space discretisation method. The superiority of this method, compared to widely used fully-explicit methods, with respect to CPU time and accuracy, is shown. Due to the high non-linearity of the governing equations a robust and fast solver for systems of nonlinear algebraic equations is needed to solve the intermediate approximations per time step. We use a nonlinear multigrid solver which shows almost h-independent convergence behaviour.

Item Type:	Article
Copyright, Publisher and Additional Information:	Copyright © 2007 Elsevier Inc. This is an author produced version of a paper subsequently published in 'Journal of Computational Physics'. Uploaded in accordance with the publisher's self-archiving policy.
Keywords:	phase-field simulation, binary alloys, mesh adaptivity, fully-implicit method, nonlinear multigrid, variable time step control
Academic Units:	The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) The University of Leeds > Faculty of Engineering (Leeds) > School of Process, Environmental and Materials Engineering (Leeds) > Institute for Materials Research (Leeds)
Depositing User:	Miss Jamie Grant
Date Deposited:	10 Mar 2009 10:43
Last Modified:	08 Feb 2013 17:06
Published Version:	http://dx.doi.org/10.1016/j.jcp.2007.01.027
Status:	Published
Publisher:	Elsevier
Refereed:	Yes
Identification Number:	10.1016/j.jcp.2007.01.027
Related URLs:	Author
URI:	http://eprints.whiterose.ac.uk/id/eprint/7940

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