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Solution to Multiscale and Multiphysics Problems: A Phase‐Field Study of Fully Coupled Thermal‐Solute‐Convection Dendrite Growth
Author(s) -
Zhang Ang,
Jiang Bin,
Guo Zhipeng,
Du Jinglian,
Wang Qigui,
Pan Fusheng,
Xiong Shoumei
Publication year - 2021
Publication title -
advanced theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.068
H-Index - 17
ISSN - 2513-0390
DOI - 10.1002/adts.202000251
Subject(s) - dendrite (mathematics) , multiphysics , convection , prandtl number , materials science , mechanics , lewis number , thermodynamics , statistical physics , physics , finite element method , mathematics , mass transfer , geometry
Solidification process is a complex phase transition problem involving multiscale and multiphysical characteristics. To investigate the complex interaction, a high‐performance numerical scheme is developed to explore the thermal‐solute‐convection interaction during solidification. Al–Cu dendrite growth with the Lewis number ≈10 4 and Prandtl number ≈10 −2 (or Schmidt number ≈10 2 ) is simulated and discussed. By constructing a multilevel data structure, this numerical scheme allows the time step magnified by 2–3 orders of magnitude in comparison with that for explicit methods. With the capacity of the acceleration strategy including parallel computing and adaptive mesh refinement, the computing efficiency can be further improved by 2–3 orders of magnitude. The combination of multilevel structure and acceleration strategy makes a problem of up to 10 9 uniform meshes much easier to handle. The coupled governing equations involving the multiscale and multiphysical characteristics are solved with high efficiency and high numerical stability, even when the solid fraction approaches 100%. Both single and multi‐dendrite growths are discussed to reveal the effect of the thermal‐solute‐convection interaction on the large‐scale 2D and 3D microstructure evolution. The presence of the liquid flow changes the distribution of both domain temperature and solute component, which changes dendrite morphology and growth dynamics.