A Scale-Separated Full-Field Monopole Method for Precipitation Modelling
Abstract
A scale-separated monopole method is developed for full-field prediction of precipitation under conditions where particle-scale diffusion fields coexist with solute variations over much larger distances. Precipitates are represented by monopole Green's-function solutions, providing a particle-based description of interacting particle growth and dissolution. The direct quasistatic formulation is validated against transient finite-difference calculations and a conventional Kampmann--Wagner numerical model, but becomes inappropriate when spatially heterogeneous particle populations generate slowly relaxing long-wavelength concentration fields. An Ewald decomposition is therefore used to separate the diffusion field by spatial scale. Screened particle-scale fields are treated quasistatically, while the complementary long-range field evolves by transient diffusion. The resulting hybrid formulation retains explicit particle-level precipitation kinetics while allowing mesoscale solute redistribution to evolve on its physical timescale. Application to Al--Sc demonstrates that a transient depletion field generated by localized precipitation can suppress subsequent nucleation and produce persistent spatial variations in precipitate number density and volume fraction.
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BibTeX
@misc{sinclair2026scaleseparated,
title = {{A Scale-Separated Full-Field Monopole Method for Precipitation Modelling}},
author = {C. W. Sinclair},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05436},
eprint = {2610.05436},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05436},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Scale-Separated Full-Field Monopole Method for Precipitation Modelling
AU - C. W. Sinclair
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05436
UR - https://arxiv.org/abs/2610.05436
AB - A scale-separated monopole method is developed for full-field prediction of precipitation under conditions where particle-scale diffusion fields coexist with solute variations over much larger distances. Precipitates are represented by monopole Green's-function solutions, providing a particle-based description of interacting particle growth and dissolution. The direct quasistatic formulation is validated against transient finite-difference calculations and a conventional Kampmann--Wagner numerical model, but becomes inappropriate when spatially heterogeneous particle populations generate slowly relaxing long-wavelength concentration fields. An Ewald decomposition is therefore used to separate the diffusion field by spatial scale. Screened particle-scale fields are treated quasistatically, while the complementary long-range field evolves by transient diffusion. The resulting hybrid formulation retains explicit particle-level precipitation kinetics while allowing mesoscale solute redistribution to evolve on its physical timescale. Application to Al--Sc demonstrates that a transient depletion field generated by localized precipitation can suppress subsequent nucleation and produce persistent spatial variations in precipitate number density and volume fraction.
ER -