Sharp-interface model for eutectic alloys. Part I: Concentration dependent surface tension

Dreyer, Wolfgang; Wagner, Barbara

doi:10.4171/ifb/121

Cited by 14 publications

(9 citation statements)

References 22 publications

(35 reference statements)

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“…The procedure is outlined with great care in [15,13]. Here, we will only sketch the main ideas for the two-dimensional case, i.e.…”

Section: Evolving Curvesmentioning

confidence: 99%

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Second order phase field asymptotics for multi-component systems

Garcke¹,

Stinner²

2006

Interfaces Free Bound.

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Abstract. We derive a phase field model which approximates a sharp interface model for solidification of a multicomponent alloy to second order in the interfacial thickness ε. Since in numerical computations for phase field models the spatial grid size has to be smaller than ε the new approach allows for considerably more accurate phase field computations than have been possible so far.In the classical approach of matched asymptotic expansions the equations to lowest order in ε lead to the sharp interface problem. Considering the equations to the next order, a correction problem is derived. It turns out that, when taking a possibly nonconstant correction term to a kinetic coefficient in the phase field model into account, the correction problem becomes trivial and the approximation of the sharp interface problem is of second order in ε. By numerical experiments, the better approximation property is well supported. The computational effort to obtain an error smaller than a given value is investigated revealing an enormous efficiency gain.

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“…The procedure is outlined with great care in [15,13]. Here, we will only sketch the main ideas for the two-dimensional case, i.e.…”

Section: Evolving Curvesmentioning

confidence: 99%

“…To determine boundary conditions for (20) and (21) on Γ(t; 0) we plug the expansions (13) and (14) into the differential equations.…”

Section: Asymptotic Analysismentioning

confidence: 99%

Second order phase field asymptotics for multi-component systems

Garcke¹,

Stinner²

2006

Interfaces Free Bound.

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“…The thickness of the interface is an artificial parameter of the problem and it is mandatory to provide both a phase-field model and a numerical scheme which converge to the sharp model interface as the thickness parameter goes to zero. The question of convergence is addressed for instance in [2] (see also [16] for the numerical aspects). The drawback of the method is that the discretization parameter has to be much smaller than the thickness parameter leading to a CPU consuming method to recover a sharp interface discretization.…”

Section: Introductionmentioning

confidence: 99%

Modeling binary alloy solidification by a random projection method

Carpy

Mathis

2018

Numerical Methods Partial

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This paper addresses the numerical modeling of the solidification of a binary alloy that obeys a liquidus-solidus phase diagram. In order to capture the moving melting front, we introduce a Lagrange projection scheme based on a random sampling projection. Using a finite volume formulation, we define accurate numerical fluxes for the temperature and concentration fields which guarantee the sharp treatment of the boundary conditions at the moving front, especially the jump of the concentration according to the liquidus-solidus diagram. We provide some numerical illustrations which assess the good behavior of the method: maximum principle, stability under CFL condition, numerical convergence toward self-similar solutions, ability to handle two melting fronts. KEYWORDS binary alloy, finite volume method, Lagrange projection scheme, random sampling projection, sharp model, solidification, Stefan problem 1 Numer Methods Partial Differential Eq. 2019;35:733-760. wileyonlinelibrary.com/journal/num

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“…So, no restrictive conditions are imposed on the initial-boundary data, unlike the case of the phase field system and the one-dimensional convective Cahn-Hilliard model. 4) In the subsystem (79), we took into account the results of [17]. Note that the above constructions remain also valid for the modified model (77)-(79) obtained from the two-dimensional model (cf.…”

Section: Commentsmentioning

confidence: 99%

Solidification and Structuresation of Instability Zones

Lukashov¹,

Radkevich²

2010

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Two mathematical crystallization models describing structure formations in instability zones are proposed and justified. The first model, based on a phase field system, describes crystallization processes in binary alloys. The second model, based on a modified Biot model of a porous medium and the convective CahnHilliard model, governs oriented crystallization. Physical interpretation and numerical analysis are discussed.

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Sharp-interface model for eutectic alloys. Part I: Concentration dependent surface tension

Cited by 14 publications

References 22 publications

Second order phase field asymptotics for multi-component systems

Second order phase field asymptotics for multi-component systems

Modeling binary alloy solidification by a random projection method

Solidification and Structuresation of Instability Zones

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