Numerical Simulations of Unsteady Crystal Growth

An efficient algorithm is developed to numerically compute solutions of problems related to crystal growth. The method is based on an integral equation formulation that involves an integration over the entire history of the growth. A direct calculation of this memory integral becomes more costly as...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1992-10, Vol.52 (5), p.1303-1320
Main Authors: Brattkus, K., Meiron, D. I.
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Boundary conditions
Coefficients
Computer simulation
Costs
Cross-disciplinary physics: materials science
rheology
Crystal growth
Differential equations
Exact sciences and technology
Heat
Integral equations
Integrals
Latent heat
Liquids
Materials science
Methods of crystal growth
physics of crystal growth
Nonlinear equations
Oscillations
Physics
Rapid quenching
Simulation
Solidification
Solids
Solutes
Temperature
Theory and models of crystal growth
physics of crystal growth, crystal morphology and orientation
Velocity
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Summary:An efficient algorithm is developed to numerically compute solutions of problems related to crystal growth. The method is based on an integral equation formulation that involves an integration over the entire history of the growth. A direct calculation of this memory integral becomes more costly as time increases, but an indirect method is presented that has a fixed operation cost per timestep. The one-dimensional procedure is tested and applied to the problem of rapid directional solidification where the nonlinear development of a recently discovered oscillatory instability is followed.
ISSN:0036-1399
1095-712X
DOI:10.1137/0152075