On a Phase-Field Model with Advection

Michal Beneš ()
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Michal Beneš: Czech Technical University in Prague, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 141-150 from Springer

Abstract: Summary In this contribution, we present a phase-field model of advected meancurvature flow and of advected pattern formation in solidification. The model is based on the approach presented in [3], where an extensive literature list on methods treating mean-curvature problems can be found. The model represents a step towards simulation of solidification processes where the melt motion is important. We give a basic mathematical information concerning the weak solution of the model equations, introduce a numerical scheme based on the Finite-Difference Method, and show several numerical studies demostrating basic qualitative effects of advection in the given context.

Keywords: Curvature Flow; Critical Radius; Gronwall Lemma; Czech Academy; Uniform Rectangular Grid (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18775-9_11

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DOI: 10.1007/978-3-642-18775-9_11

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