TY - JOUR
T1 - Efficient computation of dendritic microstructures using adaptive mesh refinement
AU - Provatas, Nikolas
AU - Goldenfeld, Nigel
AU - Dantzig, Jonathan
PY - 1998
Y1 - 1998
N2 - We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, allowing simulations on very large lattices. We present computations on a 217 × 217 lattice, but note that this is not an upper limit. Time-dependent calculations in two dimensions are in good agreement with the predictions of solvability theory for high undercoolings, but predict higher values of velocity than solvability theory at low undercooling, where transients dominate, in accord with a heuristic criterion which we derive.
AB - We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, allowing simulations on very large lattices. We present computations on a 217 × 217 lattice, but note that this is not an upper limit. Time-dependent calculations in two dimensions are in good agreement with the predictions of solvability theory for high undercoolings, but predict higher values of velocity than solvability theory at low undercooling, where transients dominate, in accord with a heuristic criterion which we derive.
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U2 - 10.1103/PhysRevLett.80.3308
DO - 10.1103/PhysRevLett.80.3308
M3 - Article
AN - SCOPUS:1842576356
SN - 0031-9007
VL - 80
SP - 3308
EP - 3311
JO - Physical review letters
JF - Physical review letters
IS - 15
ER -