Adaptive phase-field computations of dendritic crystal growth

Braun, R. J.; Murray, Bruce T.

doi:10.1016/s0022-0248(96)01059-7

Cited by 90 publications

(51 citation statements)

References 24 publications

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“…They are however more complicated than levelset methods in three spatial dimensions and it is difficult to compute accurate smooth geometric properties such as curvatures from the volume fraction alone, although we refer the reader to the interesting work of Popinet on this issue [111]. Also, we note that phase-field models have been extensively used in the case of solidification processes [20,37,57,68,69,67,94,57,112,113]. However, these models do not represent the interface in a sharp fashion, which in turn leads to a degradation of the accuracy where it matters most and impose sometimes stringent time step restrictions.…”

Section: The Stefan Problemmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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Section: The Stefan Problemmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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“…The equivalent condition for the phase equation is less straightforward, but provided M   2  D l , gives a limiting time step comparable to Equ. (18). Consequently we have adopted Equ.…”

Section: Computational Modelmentioning

confidence: 99%

“…However, if a regular meshing is utilised this can rapidly lead to an unmanageably large grid with correspondingly long computation times. One potential route to introducing a very fine grid in the interface region while preserving reasonable computational efficiency over the rest of the domain is the use of adaptive meshing techniques [18,19,20], although this is not without its own problems.…”

Section: Discusionmentioning

confidence: 99%

Quantification of mesh induced anisotropy effects in the phase-field method

Mullis

2006

Computational Materials Science

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Phase-field modelling is one of the most powerful techniques currently available for the simulation from first principles the time dependant evolution of complex solidification microstructures. However, unless care is taken the computational mesh used to solve the set of partial differential equations that result from the phase-field formulation of the solidification problem may introduce a stray, or implicit, anisotropy, which would be highly undesirable in quantitative calculations. In this paper we quantify this effect as a function of various computational parameters and subsequently suggest techniques for mitigating the effect of this stray anisotropy. 81.30.Fb, PACS:

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“…The other is to solve a system of parabolic equations in which the interface is specified by a level set of one of the variables, see, e.g. [4][5][6][7][8][9]. The later approach, also called phase-field approach, has two appealing features: (i) a broad spectrum of distinct problems that can be studied by means of a single set of equations, and (ii) the interface in these problems does not need to be tracked explicitly.…”

Section: Introductionmentioning

confidence: 99%

An alternating Crank–Nicolson method for the numerical solution of the phase‐field equations using adaptive moving meshes

Tan

Huang

2007

Numerical Methods in Fluids

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SUMMARYAn alternating Crank-Nicolson method is proposed for the numerical solution of the phase-field equations on a dynamically adaptive grid, which automatically leads to two decoupled algebraic subsystems, one is linear and the other is semilinear. The moving mesh strategy is based on the approach proposed by Li et al. (J. Comput. Phys. 2001; 170:562-588) to separate the mesh-moving and partial differential equation evolution. The phase-field equations are discretized by a finite volume method in space, and the mesh-moving part is realized by solving the conventional Euler-Lagrange equations with the standard gradient-based monitors. The algorithm is computationally efficient and has been successfully used in numerical simulations.

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Adaptive phase-field computations of dendritic crystal growth

Cited by 90 publications

References 24 publications

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

Quantification of mesh induced anisotropy effects in the phase-field method

An alternating Crank–Nicolson method for the numerical solution of the phase‐field equations using adaptive moving meshes

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