A boundary integral approach to unstable solidification

Journal Article · Fri Dec 01 04:00:00 EST 1989 · Journal of Computational Physics; (USA)

DOI:https://doi.org/10.1016/0021-9991(89)90155-1· OSTI ID:6988677

Strain, J ^[1]

---

1. Lawrence Berkeley Laboratory, Berkeley, California (USA) Department of Mathematics, University of California, Berkeley, California 94720 (USA)

We consider the supercooled Stefan problem with a general anisotropic curvature- and velocity-dependent boundary condition on the moving interface. We present numerical methods, based on an integral equation formulation and including a new algorithm for moving curves with curvature-dependent velocity. These methods compute a periodic interface with {ital O}({Delta}{ital t}) accuracy, where {Delta}{ital t} is the time step. Previous work has been limited to short time spans and achieved slightly less than {ital O}({Delta}{ital t}{sup 1/2}) accuracy. Accurate numerical results are seen to agree with the predictions of linear stability theory. This agreement has eluded previous authors, because their numerical methods suffered from grid effects and their linear stability theory was incorrect. We study the long-time evolution of an unstable interface. Our computations exhibit the beginnings of a sidebranching instability when the boundary condition includes anisotropy and tip-splitting in the isotropic case. {copyright} 1989 Academic Press, Inc.

• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6988677
• Journal Information: Journal of Computational Physics; (USA), Journal Name: Journal of Computational Physics; (USA) Vol. 85:2; ISSN 0021-9991; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
COOLING
CRYSTALS
DENDRITES
EQUATIONS
FLUIDS
INTEGRAL EQUATIONS
LIQUIDS
NUMERICAL SOLUTION
PHASE STUDIES
PHASE TRANSFORMATIONS
SOLIDIFICATION
SUBCOOLING
TWO-DIMENSIONAL CALCULATIONS