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On a Phase-Field Model with Advection

In: Numerical Mathematics and Advanced Applications

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  • Michal Beneš

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

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.

Suggested Citation

  • Michal Beneš, 2004. "On a Phase-Field Model with Advection," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 141-150, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_11
    DOI: 10.1007/978-3-642-18775-9_11
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