1991
DOI: 10.1016/0021-9991(91)90254-i
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Computation of sharp phase boundaries by spreading: The planar and spherically symmetric cases

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Cited by 68 publications
(63 citation statements)
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“…Throughout this study we use finite difference methods ([CL], [CS2]) with a fixed grid in order to isolate the issues that are of specific interest. In principle, a combination of phase field methods and adaptive grids with finite elements should provide similar accuracy at a lower cost.…”
Section: Z Oclqmentioning
confidence: 99%
“…Throughout this study we use finite difference methods ([CL], [CS2]) with a fixed grid in order to isolate the issues that are of specific interest. In principle, a combination of phase field methods and adaptive grids with finite elements should provide similar accuracy at a lower cost.…”
Section: Z Oclqmentioning
confidence: 99%
“…In other words, if one is to use the phase field equations for realistic computations the interface motion for the system with ε = 10 −4 and ε = 10 −8 must be nearly identical. This physical ansatz that the interface thickness could be stretched out by a factor of ten thousand without significantly altering the motion of the interface was suggested and confirmed numerically in [13]. Since then, phase field equations have been used for a number of applications, and appear to be one of the most viable methods for computing interface motion.…”
mentioning
confidence: 77%
“…We refer the readers to [6,10,31,32] and references therein for more details. The boundary conditions for the phase-field equations are the same as the sharp interface model for , with compatible conditions for p. For example, if Dirichlet conditions are imposed on = ± , where ± denotes the liquid and solid boundaries, respectively, then the corresponding values of p are the largest ( p + ) and smallest ( p − ) roots of…”
Section: Two-dimensional Phase-field Problemsmentioning
confidence: 99%
“…[6,7,10]). Then the two phases are characterized by p taking values close to p + and p − in each phase.…”
Section: Two-dimensional Phase-field Problemsmentioning
confidence: 99%
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