CHUNG-WEN LAN2025-12-182025-12-182026-01-3000220248https://www.scopus.com/record/display.uri?eid=2-s2.0-105021960454&origin=resultslisthttps://scholars.lib.ntu.edu.tw/handle/123456789/734748Step-flow dynamics during SiC solution growth critically shape surface morphology and defect formation, yet conventional models often average step densities or encounter front-tracking singularities, missing transient bunching and debunching. We introduce a quasi-discrete 2D/3D model that couples advection–diffusion transport with Gaussian-regularized Robin boundary conditions, representing macrosteps as localized, integral-matched sinks. Each macrostep is resolved by a few Gaussian-weighted nodes while solute transport is computed on a fine finite-element mesh, ensuring stability and mass conservation. Simulations reveal that parallel flow drives strong bunching, producing wide terraces with amplified supersaturation; bunched steps advance more slowly due to solute depletion, while high-supersaturation pockets accelerate leading steps and trigger debunching. Conversely, anti-parallel flow advects depletion upstream and preserves uniform step spacing, with no bunching across tested conditions. In three dimensions, parallel flow yields stripe coalescence, while anti-parallel flow stabilizes step trains. By quantifying terrace supersaturation's link to polytype nucleation, this robust, efficient model offers a predictive tool for optimizing step morphology and minimizing defects in high-quality SiC crystal growth.falseDebunchingGaussian Robin BCPolytype nucleationSiCSolution growthStep bunchingTerrace supersaturationjournal article10.1016/j.jcrysgro.2025.1284202-s2.0-105021960454