Application of the Level-Set Method to a Mixed-Mode and Curvature Driven Stefan Problem

D. den Ouden (), F. J. Vermolen (), L. Zhao (), C. Vuik () and J. Sietsma ()
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D. den Ouden: Materials innovation institute
F. J. Vermolen: Delft University of Technology, DIAM
L. Zhao: Materials innovation institute
C. Vuik: Delft University of Technology, DIAM
J. Sietsma: Delft University of Technology, MS&E

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 141-148 from Springer

Abstract: Abstract This study focuses on the dissolution and growth of small possibly initially non-smooth particles within a diffusive phase. The dissolution or growth of the particle is assumed to be affected by concentration gradients of a single chemical element within the diffusive phase at the particle boundary caused by diffusion and by an interface reaction. The combined formulation results in a mixed-mode formulation. The moving boundary problem is solved using a level-set method and finite-element techniques such as SUPG. The appropriate meshes are derived using a fixed background mesh and the level-set function. We experimentally show that these techniques give mass-conserving solutions in the limit of infinite resolution, give a linear experimental order of convergence, can handle arbitrary particles and give the possibility to incorporate surface tensions using the Gibbs-Thomson effect and the local curvature.

Keywords: Diffusive Phase; Stefan Problem; Circular Particle; Euler Time Integration; Standard Diffusion Equation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_15

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DOI: 10.1007/978-3-642-33134-3_15

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