TY - CHAP
T1 - Parallelization of phase-field model to simulate freezing in high-Reflow-multiscale method implementation
AU - Xu, Ying
AU - McDonough, J. M.
AU - Tagavi, K. A.
PY - 2007
Y1 - 2007
N2 - Phase-field models have been applied to phase transformation problems for decades. Many systems in nature involve multiple scales and become interesting because they exhibit different behaviors on different scales. The traditional approach for multiscale problems is to obtain, either analytically or empirically, explicit equations for the scale of interest, while eliminating other scales of the problem. The success of resulting phenomenological equations is much less spectacular for a large class of complex systems. The aim of this approach is to model the theoretical input to a coarse-grained model from a more detailed microscopic model, bypassing the necessity of empirical modeling. A macroscopic description is known, but ceases to be valid in a localized region in space and/or time, and where the microscopic description has to be used instead. A macroscopic model may not be explicitly known, or too expensive to obtain, but is known to exist- that is, there exists a set of macroscopic variables obeying a closed macroscopic model. The phase-field-like models are needed to provide details of dendrite structures on microscopic levels. © 2007
AB - Phase-field models have been applied to phase transformation problems for decades. Many systems in nature involve multiple scales and become interesting because they exhibit different behaviors on different scales. The traditional approach for multiscale problems is to obtain, either analytically or empirically, explicit equations for the scale of interest, while eliminating other scales of the problem. The success of resulting phenomenological equations is much less spectacular for a large class of complex systems. The aim of this approach is to model the theoretical input to a coarse-grained model from a more detailed microscopic model, bypassing the necessity of empirical modeling. A macroscopic description is known, but ceases to be valid in a localized region in space and/or time, and where the microscopic description has to be used instead. A macroscopic model may not be explicitly known, or too expensive to obtain, but is known to exist- that is, there exists a set of macroscopic variables obeying a closed macroscopic model. The phase-field-like models are needed to provide details of dendrite structures on microscopic levels. © 2007
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U2 - 10.1016/B978-044453035-6/50012-2
DO - 10.1016/B978-044453035-6/50012-2
M3 - Chapter
AN - SCOPUS:84882887943
SN - 9780444530356
SP - 75
EP - 82
BT - Parallel Computational Fluid Dynamics 2006
ER -