A Dynamic Mesh Algorithm for Curvature Dependent Evolving Interfaces

Nochetto, Ricardo H.; Paolini, Maurizio; Verdi, C.

doi:10.1006/jcph.1996.0025

Cited by 28 publications

(28 citation statements)

References 14 publications

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“…In those cases, the quadruple point splits into two triple points and we observe that the evolution in the second case is much slower than for the rst. This corresponds to the theoretical prediction that a quadruple point is instable if~ 23 Numerical calculation with a quadruple junction as initial condition for di erent surface tensions. 4.6.…”

Section: Numerical Simulationssupporting

confidence: 73%

“…We require a simple relation between the parameters in the functions f and and the given surface energies and mobilities. For f we will always choose the isotropic surface potential (see 28 (23) It is easily veri ed that this surface potential leads to isotropic surface energies and mobilities. As possible choices for , we either take the standard multi well bulk potential st (u) := 9 X i<j~ ij~ ij u 2 i u 2 j ; (24) or a higher order variant^ st (u) := st (u) + X i<j<k ijk u 2 i u 2 j u 2 k ; (25) or the multi obstacle potential (see 3], 13]) ob (u) := 16 2 X i<j~ ij~ ij u i u j ; (26) whenever u 2 G, and ob (u) = +1, whenever u 6 2 G, or a higher order variant ob (u) := ob (u) + X i<j<k ijk u i u j u k : (27) For the obstacle potentials the system of Allen{Cahn equations (8) has to be replaced by a parabolic variational inequality.…”

Section: The Multi Phase Field Conceptmentioning

confidence: 99%

“…Triple junction motion driven by surface tension and bulk driving forces. 23 and~ 14 . In those cases, the quadruple point splits into two triple points and we observe that the evolution in the second case is much slower than for the rst.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions

Garcke¹,

Nestler²,

Stoth³

1999

SIAM J. Appl. Math.

217

190

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Abstract. We present numerical simulations which support the formal asymptotic analysis relating a multi order parameter Allen{Cahn system to a multi phase interface problem with curvature dependent evolution of the interfaces and angle conditions at triple junctions. Within the gradient energy of the Allen{Cahn system, the normal to an interface between phases i and j is modeled by the irreducible representations (u i ru j ? u j ru i )=ju i ru j ? u j ru i j, where u i and u j are the i{th and j{th components of the vectorial order parameter u 2 IR N .In the vectorial case, the dependence of the limiting surface tensions and mobilities on the bulk potentials of the Allen{Cahn system is not given explicitly, but in terms of all the N components of the planar stationary wave solutions. One of the issues of this paper is to nd bulk potentials which allow a rather easy access to the resulting surface tensions and mobilities.We compare numerical computations for planar and circular phase boundaries in two and three phase systems. The di erence is, that in a three phase system, the third phase generally will be present in the interfacial region between two other phases. We demonstrate how this in uences the solutions. In addition, we calculate the evolution of triple and quadruple junctions in three and four phase systems. Finally, we show a simulation of grain growth starting from many grains initially.

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Section: Numerical Simulationssupporting

confidence: 73%

Section: The Multi Phase Field Conceptmentioning

confidence: 99%

See 1 more Smart Citation

A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions

Garcke¹,

Nestler²,

Stoth³

1999

SIAM J. Appl. Math.

217

190

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show abstract

“…[4,5,18,19] are examples of this). This can lead to more efficient computation, but at the expense of complicating the implementation of the underlying numerical method.…”

Section: Introductionmentioning

confidence: 91%

Nonlinear Preconditioning for Diffuse Interfaces

Glasner

2001

Journal of Computational Physics

105

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“…One example is = |C − 1/2| 3/2 |C + 1/2| 3/2 , for which bulkphase has square root behavior. Another is the double obstacle energy recently used by Oono and Puri [19] and Nochetto [18]. This…”

Section: Phase-field Surface Tension and Interface Widthmentioning

confidence: 99%