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Most heat transfer models for bulk crystal growth rely on the classicalStefan formulation to evaluate interface motion during phase change. However,when the interface is non-smooth the use of the classical Stefan formulationmay lead to singularities. To address this problem, we propose a simulationmodel based on the weak formulation of the Stefan problem. Numerical solutionsof the weak Stefan formulation are obtained using the finite volume method.This approach provides an energy conserving discretization scheme thataccurately evaluates heat transfer around non-smooth interfaces. We apply theweak formulation to numerically simulate the solidification of silicon in thehorizontal ribbon growth process. Results exhibit a limitation on the ribbon'spull speed, which previous classical Stefan models have failed to demonstrate.A comparison of heat transfer between radiation and gas cooling shows that gascooling increases the pull speed limit for the same amount of heat removed.

Weak Stefan Formulation for Bulk Crystal Growth with Non-smooth Interfaces