A unified multirate lattice Boltzmann framework for thermosolutal dendritic solidification

Abstract

Thermosolutal dendritic solidification involves interface evolution, solute diffusion, heat transfer, and melt flow over markedly different time scales. In lattice Boltzmann simulations, a single numerical time interval may place different transport processes in unfavorable relaxation ranges, while asynchronous updates require consistent transfer of phase-change contributions. To address these issues, a unified multirate multiple-relaxation-time lattice Boltzmann method is developed for thermal, solutal, and thermosolutal dendritic solidification. The coupled fields share a common moment-space framework but evolve at different update rates. The concentration and temperature source terms are separated into transport-related and phase-change contributions, and each resolved phase increment is used to immediately transfer the corresponding solutal and latent-heat contributions. The method reproduces characteristic dendritic morphologies and tip-velocity trends under pure diffusion and forced convection, with weak sensitivity to the tested update factors. Directional solidification over Lewis numbers Le=1--1000 captures the transition from nearly planar to cellular and strongly branched growth, including vertically aligned dendrites and solute-rich interdendritic channels for saline water, in qualitative agreement with experiments. Source-coupling ablation shows that delayed coarse-step transfer produces increasingly strong local source pulses and eventual loss of numerical stability as time-scale separation increases, whereas phase-step instantaneous transfer remains stable over the tested conditions. These results demonstrate the applicability of the proposed framework to dendritic solidification with strongly separated transport time scales. The source code is publicly available in the \emph{DendriteLBM} repository.

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BibTeX RIS

BibTeX

@misc{liu2026unified,
  title = {{A unified multirate lattice Boltzmann framework for thermosolutal dendritic solidification}},
  author = {Yang Liu and Xiaomin Wu and Chengjie Zhan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25670},
  eprint = {2609.25670},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25670},
}

RIS

TY  - UNPB
TI  - A unified multirate lattice Boltzmann framework for thermosolutal dendritic solidification
AU  - Yang Liu
AU  - Xiaomin Wu
AU  - Chengjie Zhan
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25670
UR  - https://arxiv.org/abs/2609.25670
AB  - Thermosolutal dendritic solidification involves interface evolution, solute diffusion, heat transfer, and melt flow over markedly different time scales. In lattice Boltzmann simulations, a single numerical time interval may place different transport processes in unfavorable relaxation ranges, while asynchronous updates require consistent transfer of phase-change contributions. To address these issues, a unified multirate multiple-relaxation-time lattice Boltzmann method is developed for thermal, solutal, and thermosolutal dendritic solidification. The coupled fields share a common moment-space framework but evolve at different update rates. The concentration and temperature source terms are separated into transport-related and phase-change contributions, and each resolved phase increment is used to immediately transfer the corresponding solutal and latent-heat contributions. The method reproduces characteristic dendritic morphologies and tip-velocity trends under pure diffusion and forced convection, with weak sensitivity to the tested update factors. Directional solidification over Lewis numbers Le=1--1000 captures the transition from nearly planar to cellular and strongly branched growth, including vertically aligned dendrites and solute-rich interdendritic channels for saline water, in qualitative agreement with experiments. Source-coupling ablation shows that delayed coarse-step transfer produces increasingly strong local source pulses and eventual loss of numerical stability as time-scale separation increases, whereas phase-step instantaneous transfer remains stable over the tested conditions. These results demonstrate the applicability of the proposed framework to dendritic solidification with strongly separated transport time scales. The source code is publicly available in the \emph{DendriteLBM} repository.
ER  -

Abstract

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