Solution to Multiscale and Multiphysics Problems: A Phase‐Field Study of Fully Coupled Thermal‐Solute‐Convection Dendrite Growth

Abstract

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 ≈104 and Prandtl number ≈10−2 (or Schmidt number ≈102) 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 109 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.

Large-scale phase-field simulations for dendrite growth: A review on current status and future perspective

“…In simulations with liquid flow, we usually need a significantly larger computational domain than that for purely diffusive conditions, and AMR is very effective under such conditions. Guo et al have been actively developing parallel-AMR [88], and recently applied it to dendrite growth under thermosolutal convection [89]. We developed a multi-GPU parallel-AMR scheme [37] for purely diffusive PF simulations, in which octree block decomposition and dynamic load balancing were incorporated in the code [90].…”

High-performance GPU computing of phase-field lattice Boltzmann simulations for dendrite growth with natural convection

“…Parallel computing using multiple graphics processing units (GPUs) of the PF-lattice Boltzmann (LB) model [45,46], coupled with the PF and LB methods enabled us to compute the growth of multiple columnar dendrites with natural convection [8,47,48]. Adaptive mesh refinement (AMR) is a powerful numerical scheme for reducing the computational cost of PF simulations [49][50][51][52][53]. Recently, we implemented AMR in parallel computing with multiple GPUs (parallel-GPU AMR) for the PF and PF-LB methods [54][55][56].…”

Dendrite Pattern Formation of Sodium Chloride Crystal

“…Other examples are dendrites such as copper dendrites [ 4 ] and the electrochemical deposition of zinc [ 5 , 6 , 7 ]. The formation of these dendrite patterns is understood in terms of diffusion-limited aggregation [ 8 ] and recently several works have succeeded in reproducing such pattern formations numerically [ 9 , 10 ].…”